tag:blogger.com,1999:blog-43753887398613381502024-03-19T13:06:15.336-05:00Origami y MatemáticasJaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.comBlogger50125tag:blogger.com,1999:blog-4375388739861338150.post-43444671916822100642023-09-15T08:02:00.000-05:002023-09-15T08:02:02.029-05:00Poliedros Platónicos: Icosaedro<h1 style="text-align: center;"><span style="font-size: 20pt; line-height: 107%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Icosaedro<o:p></o:p></span></h1><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="298" src="https://www.youtube.com/embed/lCk9-uxi6Cs" width="475" youtube-src-id="lCk9-uxi6Cs"></iframe></div><br /><span style="font-size: 20pt; line-height: 107%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="310" src="https://www.youtube.com/embed/17n36I_THwk" width="513" youtube-src-id="17n36I_THwk"></iframe></div><br /><span style="font-size: 20pt; line-height: 107%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="294" src="https://www.youtube.com/embed/Ws_ujEBCxf4" width="480" youtube-src-id="Ws_ujEBCxf4"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="299" src="https://www.youtube.com/embed/5L7d8lnYywI" width="487" youtube-src-id="5L7d8lnYywI"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span><span style="background-color: transparent; color: #050505; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Este sólido hace parte de la familia de los sólidos regulares o poliedros Platónicos </span><span style="background-color: transparent; color: #3b170b; font-family: Merriweather, Georgia, serif; font-size: 15.3333px; text-align: justify;">(</span><a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" style="background: transparent; color: #729c0b; font-family: Merriweather, Georgia, serif; font-size: 15.3333px; text-align: justify; text-decoration-line: none;" target="_blank">ver Poliedros Platónicos y Arquimedianos</a><span style="background-color: transparent; color: #3b170b; font-family: Merriweather, Georgia, serif; font-size: 15.3333px; text-align: justify;">)</span><span style="background-color: transparent; color: #050505; font-family: "Times New Roman", serif; font-size: 14pt;">, conocidos con este nombre en honor al filósofo griego Platón, a quien se le atribuye ser el primero en estudiarlos. Es un poliedro convexo, tiene 20 caras con forma de triángulos equiláteros, tiene 20 aristas y 12 vértices.</span></p><div class="separator" style="clear: both; text-align: center;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><iframe allowfullscreen="" class="BLOG_video_class" height="340" src="https://www.youtube.com/embed/NwwTJGOeI50" width="486" youtube-src-id="NwwTJGOeI50"></iframe></span></div><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span><p></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-dwQ7ExJCaTc/YJFj66Ew2lI/AAAAAAAAICI/t6fA2ZyUS_EIB_2RsTtNIxcikfgTrFHoQCLcBGAsYHQ/s2048/Tron.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1365" data-original-width="2048" src="https://1.bp.blogspot.com/-dwQ7ExJCaTc/YJFj66Ew2lI/AAAAAAAAICI/t6fA2ZyUS_EIB_2RsTtNIxcikfgTrFHoQCLcBGAsYHQ/s320/Tron.jpg" width="320" /></a></div><div style="text-align: center;"><a href="https://www.instagram.com/jaimeninob/"><span> </span>https://www.instagram.com/jaimeninob/</a></div><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Animación del
Icosaedro<o:p></o:p></span></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-v7pDyLUN3jc/YJFiw_Kw33I/AAAAAAAAIB8/zj7aihj2qPIR723SuyE6SYsO64pjjpXdwCLcBGAsYHQ/s643/icosaedro%2B2.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="582" data-original-width="643" src="https://1.bp.blogspot.com/-v7pDyLUN3jc/YJFiw_Kw33I/AAAAAAAAIB8/zj7aihj2qPIR723SuyE6SYsO64pjjpXdwCLcBGAsYHQ/s320/icosaedro%2B2.gif" width="320" /></a></div><br /><p></p><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Animación de uno de
los desarrollos del Icosaedro.<o:p></o:p></span></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-tbQfBzqnxMI/YJFiRn5SeZI/AAAAAAAAIBw/Ax33bUvszHsW_R1h0kqPvmyyXEIKPBfggCLcBGAsYHQ/s643/icosaedro%2B1.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="582" data-original-width="643" src="https://1.bp.blogspot.com/-tbQfBzqnxMI/YJFiRn5SeZI/AAAAAAAAIBw/Ax33bUvszHsW_R1h0kqPvmyyXEIKPBfggCLcBGAsYHQ/s320/icosaedro%2B1.gif" width="320" /></a></div><br /><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Desarrollo del
icosaedro:<o:p></o:p></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-VGZrPbzweAQ/YJFhxTdmnoI/AAAAAAAAIBk/6uhAgGraPQ0g7G_3jcPL2shCOUGNc94YQCLcBGAsYHQ/s585/icosaedro%2B3.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="506" data-original-width="585" height="277" src="https://1.bp.blogspot.com/-VGZrPbzweAQ/YJFhxTdmnoI/AAAAAAAAIBk/6uhAgGraPQ0g7G_3jcPL2shCOUGNc94YQCLcBGAsYHQ/w320-h277/icosaedro%2B3.gif" width="320" /></a></div><br /><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; mso-margin-top-alt: auto;"><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">En todo poliedro regular, el número de caras más el número de vértices,
es igual al número de aristas más 2. Se conoce como característica de Euler,
una propiedad topológica.</span><span style="font-family: "Times New Roman", serif; font-size: 14pt;"><o:p></o:p></span></p>
<p align="center" class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; mso-margin-top-alt: auto; text-align: center;"><span style="font-family: "Times New Roman", serif; font-size: 14pt;">C + V = A + 2<o:p></o:p></span></p>
<p align="center" class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; mso-margin-top-alt: auto; text-align: center;"><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> donde: C =
número de caras; V = número de vértices; A = número de aristas</span><span style="font-family: "Times New Roman", serif; font-size: 14pt;"><o:p></o:p></span></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 14pt;">El área y volumen del icosaedro de en función de la longitud de su
arista son</span><span style="background-color: transparent;"> </span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-zovV187TxHE/YJFk-ES6B0I/AAAAAAAAICU/d7rBpfLZX7AY3AaJVvtwOtjCxQ5qj1JVQCLcBGAsYHQ/s909/icosaedro%2B%25C3%25A1rea%2By%2Bvolumen.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="428" data-original-width="909" height="189" src="https://1.bp.blogspot.com/-zovV187TxHE/YJFk-ES6B0I/AAAAAAAAICU/d7rBpfLZX7AY3AaJVvtwOtjCxQ5qj1JVQCLcBGAsYHQ/w400-h189/icosaedro%2B%25C3%25A1rea%2By%2Bvolumen.PNG" width="400" /></a></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="font-family: Merriweather, Georgia, serif; font-size: 16px;">Si lo quieres construir en papel, esto videos te pueden ayudar</span></p><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="325" src="https://www.youtube.com/embed/mUgN0raylws" width="506" youtube-src-id="mUgN0raylws"></iframe></div><br /><span style="font-size: 20pt; line-height: 28.5333px; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="font-family: Merriweather, Georgia, serif; font-size: 16px;"></span></p><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="292" src="https://www.youtube.com/embed/mSzZBChZVag" width="474" youtube-src-id="mSzZBChZVag"></iframe></div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="327" src="https://www.youtube.com/embed/bvy1MzSw1BY" width="511" youtube-src-id="bvy1MzSw1BY"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="355" src="https://www.youtube.com/embed/UTZFGFMiPqk" width="487" youtube-src-id="UTZFGFMiPqk"></iframe></div><br /><span style="font-family: Merriweather, Georgia, serif; font-size: 16px;"><br /></span><p></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="316" src="https://www.youtube.com/embed/-BCHPMdcleo" width="422" youtube-src-id="-BCHPMdcleo"></iframe></div><br /><span style="font-family: Merriweather, Georgia, serif; font-size: 16px;"><br /></span><p></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="319" src="https://www.youtube.com/embed/bwRffYBHck4" width="489" youtube-src-id="bwRffYBHck4"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="315" src="https://www.youtube.com/embed/YOISi-2VYnw" width="501" youtube-src-id="YOISi-2VYnw"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="318" src="https://www.youtube.com/embed/HSC00CjOl1U" width="495" youtube-src-id="HSC00CjOl1U"></iframe></div><br /><span style="font-family: Merriweather, Georgia, serif; font-size: 16px;"><br /></span><p></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><br /></p><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 11.5pt; line-height: 107%; mso-ansi-language: ES-CO; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Esta publicación incluye imágenes
I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www
.peda.com/polypro)</span><br /><span style="background-color: transparent;"><br /></span><p></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-23296725280132922762023-05-31T11:33:00.000-05:002023-05-31T11:33:14.108-05:00Poliedros: Construcción de un Tetraedro Regular<h1>Tetraedro</h1><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="280" src="https://www.youtube.com/embed/fTf4mQKwh0Q" width="453" youtube-src-id="fTf4mQKwh0Q"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><p class="MsoNormal"><span face=""Segoe UI Historic", sans-serif">Hace parte de la familia de los sólidos regulares o poliedros Platónicos </span><span face="Helvetica, sans-serif">(<a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">ver Poliedros Platónicos y Arquimedianos</a>)</span><span face="Helvetica, sans-serif"> </span>, conocidos con este nombre en honor al filósofo griego Platón, a quien se le atribuye ser el primero en estudiarlos. Es un poliedro convexo, tiene 4 caras con forma de triángulos equiláteros, tiene 16 aristas y 4 vértices.</p><p class="MsoNormal">Instrucciones para construirlo en origami en los siquientes enlaces</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="286" src="https://www.youtube.com/embed/dJmUWZ_y0Fk" width="446" youtube-src-id="dJmUWZ_y0Fk"></iframe></div><p class="MsoNormal"><br /></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="293" src="https://www.youtube.com/embed/5b3SyAD4N6o" width="488" youtube-src-id="5b3SyAD4N6o"></iframe></div><p class="MsoNormal"><br /></p><div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="283" src="https://www.youtube.com/embed/H9sI5fp-_cA" width="439" youtube-src-id="H9sI5fp-_cA"></iframe></div><p class="MsoNormal"><br /></p><div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="321" src="https://www.youtube.com/embed/LyrP0o_PU3c" width="438" youtube-src-id="LyrP0o_PU3c"></iframe></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="348" src="https://www.youtube.com/embed/0mZVFK9rFf0" width="419" youtube-src-id="0mZVFK9rFf0"></iframe></div><div><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="351" src="https://www.youtube.com/embed/LTus6iMEG4k" width="423" youtube-src-id="LTus6iMEG4k"></iframe></div><br /><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><span face=""Helvetica",sans-serif"> </span></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-90981497172970228642023-05-31T11:31:00.000-05:002023-05-31T11:31:45.854-05:00Poliedros: Construcción de cubos en origami<p></p><h1 style="background: white; margin-bottom: 0cm; text-align: left; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Cubo</span></h1><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="314" src="https://www.youtube.com/embed/c44OVuRnygU" width="499" youtube-src-id="c44OVuRnygU"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><div style="color: black; font-size: medium;"><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">C</span><span face=""Segoe UI Historic", sans-serif" style="color: #050505; font-size: 11.5pt;">ubo o Hexaedro regular, hace parte de la familia de los sólidos regulares o poliedros Platónicos </span><span face="Helvetica, sans-serif" style="background-color: transparent; color: #3b170b; font-size: 11.5pt; text-align: justify;">(<a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">ver Poliedros Platónicos y Arquimedianos</a>)</span><span face="Helvetica, sans-serif" style="background-color: transparent; color: #3b170b; font-size: 11.5pt; text-align: justify;"> </span><span style="color: #050505; font-size: 11.5pt;">, conocidos con este nombre en honor al filósofo griego Platón, a quien se le atribuye ser el primero en estudiarlos. Es un poliedro convexo, tiene 6 caras con forma de cuadrados, tiene 12 aristas y 8 vértices.</span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-kc0Bdezd5p4/YC8rYnS5X-I/AAAAAAAAHrQ/VjZ2Oq3gflcZcb7CcSYzfHB9b4b2G550gCLcBGAsYHQ/s640/cubo%2Baristas.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="394" data-original-width="640" src="https://1.bp.blogspot.com/-kc0Bdezd5p4/YC8rYnS5X-I/AAAAAAAAHrQ/VjZ2Oq3gflcZcb7CcSYzfHB9b4b2G550gCLcBGAsYHQ/s320/cubo%2Baristas.gif" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-K8dSKEIy1QU/YC8rYlzbxoI/AAAAAAAAHrY/v8BnISI5aQ4On7DFO2l4ookpsV8c4bErgCLcBGAsYHQ/s640/Cubo.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="394" data-original-width="640" src="https://1.bp.blogspot.com/-K8dSKEIy1QU/YC8rYlzbxoI/AAAAAAAAHrY/v8BnISI5aQ4On7DFO2l4ookpsV8c4bErgCLcBGAsYHQ/s320/Cubo.gif" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-DWSYSCXCoow/YC8rYpV-i8I/AAAAAAAAHrU/C203VOaKnIE5nnUR5Mv5YeNKNLaUfaa_ACLcBGAsYHQ/s640/Red%2BBidimensional%2BCubo.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="394" data-original-width="640" src="https://1.bp.blogspot.com/-DWSYSCXCoow/YC8rYpV-i8I/AAAAAAAAHrU/C203VOaKnIE5nnUR5Mv5YeNKNLaUfaa_ACLcBGAsYHQ/s320/Red%2BBidimensional%2BCubo.gif" width="320" /></a></div><br /><p></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;">El área y volumen del cubo de en función de la longitud de su arista son</span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/--0NTBoGypqw/YC8rwMj3qYI/AAAAAAAAHro/91e_Vm-cuhUc6TBQTPjbORDn3Fg-Fy5SwCLcBGAsYHQ/s468/cubo.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="398" data-original-width="468" src="https://1.bp.blogspot.com/--0NTBoGypqw/YC8rwMj3qYI/AAAAAAAAHro/91e_Vm-cuhUc6TBQTPjbORDn3Fg-Fy5SwCLcBGAsYHQ/s320/cubo.PNG" width="320" /></a></div></div><div class="separator" style="clear: both; color: black; font-size: medium; text-align: center;"><span style="text-align: left;">Si los quieres construir en papel, estos videos te pueden ayudar</span></div><div class="separator" style="clear: both; color: black; font-size: medium; text-align: center;"><span style="text-align: left;"><div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="292" src="https://www.youtube.com/embed/Izu7WguHgsU" width="480" youtube-src-id="Izu7WguHgsU"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="289" src="https://www.youtube.com/embed/juj3f2ZHl6Q" width="448" youtube-src-id="juj3f2ZHl6Q"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="297" src="https://www.youtube.com/embed/e3X2XWWYcbA" width="468" youtube-src-id="e3X2XWWYcbA"></iframe></div></div><div><br /></div></span></div></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="307" src="https://www.youtube.com/embed/HRo8iD5KsRg" width="497" youtube-src-id="HRo8iD5KsRg"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="314" src="https://www.youtube.com/embed/FV2lGdJa1EE" width="517" youtube-src-id="FV2lGdJa1EE"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="296" src="https://www.youtube.com/embed/2iojw4bTnD4" width="486" youtube-src-id="2iojw4bTnD4"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><div style="color: black; font-size: medium;"><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><br /></p></div></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="304" src="https://www.youtube.com/embed/BzIZX8askKk" width="414" youtube-src-id="BzIZX8askKk"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="338" src="https://www.youtube.com/embed/2bzMYHrF1ck" width="464" youtube-src-id="2bzMYHrF1ck"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="312" src="https://www.youtube.com/embed/Y2Qlyw911Q8" width="431" youtube-src-id="Y2Qlyw911Q8"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><div style="color: black; font-size: medium;"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="352" src="https://www.youtube.com/embed/Os_IqCSLZaQ" width="453" youtube-src-id="Os_IqCSLZaQ"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div style="color: black; font-size: medium;"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="342" src="https://www.youtube.com/embed/gO8Ck6IHU-M" width="434" youtube-src-id="gO8Ck6IHU-M"></iframe></div><div><br /></div></div></span></div><div><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="316" src="https://www.youtube.com/embed/BMtr7-BVFzA" width="430" youtube-src-id="BMtr7-BVFzA"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/OCVhrdv6QSg" width="438" youtube-src-id="OCVhrdv6QSg"></iframe></div>Construcción de cubo origami<br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/OsF5AttpbGo" width="439" youtube-src-id="OsF5AttpbGo"></iframe></div><div style="text-align: center;"><br /></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/5WfwfP_3x-c" width="410" youtube-src-id="5WfwfP_3x-c"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/8FlLCOGoTLg" width="406" youtube-src-id="8FlLCOGoTLg"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/GMrTjbhRDa4" width="420" youtube-src-id="GMrTjbhRDa4"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/4_Pmh0bttBk" width="320" youtube-src-id="4_Pmh0bttBk"></iframe></div><br /><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/9MD0RhXxXR8" width="320" youtube-src-id="9MD0RhXxXR8"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/QtuQLNUCbyg" width="320" youtube-src-id="QtuQLNUCbyg"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/KDYeH2M9TkQ" width="320" youtube-src-id="KDYeH2M9TkQ"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="303" src="https://www.youtube.com/embed/12UKabjAYbo" width="443" youtube-src-id="12UKabjAYbo"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="338" src="https://www.youtube.com/embed/oWvcUCHvskw" width="429" youtube-src-id="oWvcUCHvskw"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="320" src="https://www.youtube.com/embed/WJbPGH0OvFI" width="418" youtube-src-id="WJbPGH0OvFI"></iframe></div><br /><div style="text-align: center;"><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="293" src="https://www.youtube.com/embed/g8s1fJrv6D0" width="463" youtube-src-id="g8s1fJrv6D0"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="331" src="https://www.youtube.com/embed/8eP5YOEe7CQ" width="502" youtube-src-id="8eP5YOEe7CQ"></iframe></div><div><br /></div></div></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-56951749899170055412023-05-31T11:29:00.000-05:002023-05-31T11:29:44.764-05:00Problemas de Triangulos rectángulos solucionados con razones trigonométricas<p> Un excursionista se encuentra a la orilla de un río, como se muestra en la siguiente figura. Halla la altura del árbol.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/UAE0athjO4A" width="452" youtube-src-id="UAE0athjO4A"></iframe></div><div><br /></div>Una persona de 1,75 m de estatura observa un avión como se muestra en la figura. ¿A qué altura aproximada, con respecto al suelo se encuentra el avión?<div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/pKBzGzmhltg" width="464" youtube-src-id="pKBzGzmhltg"></iframe></div><br /><p></p></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-16700433886336677992023-05-31T11:24:00.000-05:002023-05-31T11:24:28.847-05:00Poliedros: Cuboctaedro<h1 style="text-align: center;">Cuboctaedro</h1><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="302" src="https://www.youtube.com/embed/5EPn7VvjpM8" width="497" youtube-src-id="5EPn7VvjpM8"></iframe></div><br /><div style="text-align: center;"><br /></div><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="308" src="https://www.youtube.com/embed/j1SbpDAXkYc" width="492" youtube-src-id="j1SbpDAXkYc"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div><br /></div><div><div><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; line-height: 18.5467px; text-align: justify;">El Cuboctaedro hace parte de la familia de los sólidos semirregulares o poliedros arquimedianos, c</span><span style="color: #202122; font-family: "Times New Roman",serif; font-size: 13pt; line-height: 18.5467px; text-align: justify;">onocidos con este nombre en honor al matemático Arquímedes, quien describió extensamente estos cuerpos. </span><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; line-height: 18.5467px; text-align: justify;">Es un poliedro convexo, que se obtiene </span><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 13pt; line-height: 18.5467px; text-align: justify;">truncando (cortando) los vértices del cubo a la mitad de la longitud de la </span><span style="font-family: "Times New Roman", serif; font-size: 13pt; line-height: 18.5467px; text-align: justify;">arista. Se eliminan cuatro tetraedros, uno en cada vértice. </span><span style="font-family: "Times New Roman", serif; font-size: 13pt; line-height: 18.5467px; text-align: justify;">Se eliminan cuatro pirámides de base triangular, una en cada vértice</span><span style="font-family: "Times New Roman",serif; font-size: 13pt; line-height: 18.5467px; mso-fareast-language: ES-CO; text-align: justify;"> tiene el mismo número de caras que un Cuboctaedro: 14 caras, 8 de ellas son cuadradas y 6 de ellas triángulos equiláteros.</span></div><div><p class="MsoNormal"><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 17.12px; mso-fareast-language: ES-CO;"> </span></p><div align="center"><table border="1" cellpadding="0" cellspacing="0" class="MsoTable15Grid4Accent2" style="border-collapse: collapse; border: none; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 280px;"><tbody><tr><td colspan="2" style="background: rgb(237, 125, 49); border: 1pt solid rgb(237, 125, 49); mso-background-themecolor: accent2; mso-border-alt: solid #ED7D31 .5pt; mso-border-themecolor: accent2; padding: 0cm 5.4pt; width: 210pt;" valign="top" width="280"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 5; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 16pt;">Cuboctaedro<o:p></o:p></span></b></p></td></tr><tr><td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 68; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Caras</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p></td><td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 64; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">14</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p></td></tr><tr><td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Aristas<o:p></o:p></span></b></p></td><td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">24<o:p></o:p></span></b></p></td></tr><tr><td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 68; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Vértices</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p></td><td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 64; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">12</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p></td></tr><tr><td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Configuración de vértices<o:p></o:p></span></b></p></td><td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187"><p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Uniforme de orden 3<br />2 Triángulos</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><br />2 Cuadrados<o:p></o:p></span></b></p></td></tr></tbody></table></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #3b170b; font-size: 13pt;"> </span></p></div><div style="text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjMY5Og9qis41WJE60-PjvnYh_Rqalmj9WFSgxIA4efjIjztk-Hb1ms1UWGeQvKvUemhQTrzMpnymLlbi1HjqyT4E1lnIwAeQLWSGDR4x5tXGrGVWY_ctIDUigx4N0ko9DTeaXK9tPVc6NY2vcM3vg_6mUH3CtGDjMaCeU5wV3ui80I1CiDK0UrMLCA=s434" style="margin-left: 1em; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj7qIQDBjIPnVWvT4Kx5AdMHCMZ0Dq6RI5_4lKqHqH72EfbaCtMSHocAMlflu6Q0ZXbLZSGU5nPuqq5L4F0wdjsidLoI4_c1ZEG7m36vL42pfM8h-JNSLpcIwNLJ2zWL6TXtU_tT9qjIgR7VXtFI3z77ffvDeOhBnNKElpfy0Q2t1XwtvKg91ojC6od=s434" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="313" data-original-width="434" height="289" src="https://blogger.googleusercontent.com/img/a/AVvXsEj7qIQDBjIPnVWvT4Kx5AdMHCMZ0Dq6RI5_4lKqHqH72EfbaCtMSHocAMlflu6Q0ZXbLZSGU5nPuqq5L4F0wdjsidLoI4_c1ZEG7m36vL42pfM8h-JNSLpcIwNLJ2zWL6TXtU_tT9qjIgR7VXtFI3z77ffvDeOhBnNKElpfy0Q2t1XwtvKg91ojC6od=w400-h289" width="400" /></a></div><br /><br /><div><span style="font-size: x-large;">Si quieres construir uno te dejo algunos videos</span></div></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="314" src="https://www.youtube.com/embed/ZG1J0IHRsW8" width="445" youtube-src-id="ZG1J0IHRsW8"></iframe></div><br /><div><br /></div><div class="separator" style="clear: both; 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text-align: center;"><br /></div><div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="311" src="https://www.youtube.com/embed/Od2H1ftKukU" width="481" youtube-src-id="Od2H1ftKukU"></iframe></div></div></div><div style="text-align: left;"><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Esta publicación<span style="mso-spacerun: yes;"> </span>incluye imágenes
I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www.peda.com/polypro)<o:p></o:p></span></p><br /></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-58740328322193223042023-05-31T11:17:00.000-05:002023-05-31T11:17:06.549-05:00Reto Cartelera Matemática - Triangulos rectángulos<p> </p><p>La figura está compuesta por cuatro triángulos rectángulos congruentes. Determine el perímetro del octágono.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSH4CvTCZiG9fOFaKr5a3bwzCn8gC9GzVE9iS2qh2Xm2_wawk0HQ3eJ9UVjclVpYcPi_bj2ZmzMbtkoWMG3p8_Mtg4IcHNtOegzTwObmnXbL9t0QB_uqeHuBDF_F9coi7_RswXOs19m17rmgJKg-x4lNlXyE23vffCa9uVFWPHZla2jE_wgmF_6oLS/s965/96.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="353" data-original-width="965" height="234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSH4CvTCZiG9fOFaKr5a3bwzCn8gC9GzVE9iS2qh2Xm2_wawk0HQ3eJ9UVjclVpYcPi_bj2ZmzMbtkoWMG3p8_Mtg4IcHNtOegzTwObmnXbL9t0QB_uqeHuBDF_F9coi7_RswXOs19m17rmgJKg-x4lNlXyE23vffCa9uVFWPHZla2jE_wgmF_6oLS/w640-h234/96.jpg" width="640" /></a></div><br /><p></p><p><br /></p><p></p><div style="text-align: center;">Solución</div><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/snQCvqvUPG0" width="455" youtube-src-id="snQCvqvUPG0"></iframe></div><br /><p></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-73121828377981589042023-03-15T22:10:00.000-05:002023-03-15T22:10:09.968-05:00Poliedros: Construcción de icosaedro truncado - Características<h1 style="background: white; margin-bottom: 0cm; text-align: center; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Icosaedro Truncado</span></h1><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="301" src="https://www.youtube.com/embed/EjuEqLHuc7I" width="459" youtube-src-id="EjuEqLHuc7I"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 16.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: justify; vertical-align: baseline;"><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;">El icosaedro truncado es uno de los
trece poliedros (<a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">ver Poliedros Platónicos y Arquimedianos</a>)</span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;"> </span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;">de Arquímedes, también conocidos como poliedros semirregulares </span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;"> </span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;">o poliedros
arquimedianos. </span><span face="Helvetica, sans-serif" style="background-color: transparent; color: #3b170b; font-size: 11.5pt; text-align: left;">Se forma al truncar
(cortar) los vértices de un icosaedro, a un tercio de cada arista, de este truncamiento se forman 32
caras (</span><span face="Helvetica, sans-serif" style="background-color: transparent; color: #3b170b; font-size: 11.5pt; text-align: left;">20 hexágonos regulares y 12
pentágonos regulares), tiene 90 aristas y 60 vértices.</span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt;"><br /></span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-qAMzNV0oN7U/UjpdrA-IO1I/AAAAAAAAAp4/Ih-8cg3IibM/s1600/icosaedro+truncado.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="152" src="http://2.bp.blogspot.com/-qAMzNV0oN7U/UjpdrA-IO1I/AAAAAAAAAp4/Ih-8cg3IibM/s320/icosaedro+truncado.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; line-height: 107%; mso-ansi-language: ES-CO; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Es común encontrar este sólido
en los balones de fútbol</span></div><div class="separator" style="clear: both; text-align: left;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; line-height: 107%; mso-ansi-language: ES-CO; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-6A9EcKq6tck/YCRuO76zoZI/AAAAAAAAHoE/Bj3nL6gpTcAyYajRcqbs2MnCumSj9cr3ACLcBGAsYHQ/s1920/soccer-ball-2844880_1920.png" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: times;"><img border="0" data-original-height="962" data-original-width="1920" src="https://1.bp.blogspot.com/-6A9EcKq6tck/YCRuO76zoZI/AAAAAAAAHoE/Bj3nL6gpTcAyYajRcqbs2MnCumSj9cr3ACLcBGAsYHQ/s320/soccer-ball-2844880_1920.png" width="320" /></span></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">El área y volumen del icosaedro
truncado se calcula con las siguientes expresiones en función de la longitud de la arista</span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-CPoTLNw8LeE/YCRxnHjf1fI/AAAAAAAAHoQ/wog1dCNJDtgJfqX_bzBom7z8nap3C-41gCLcBGAsYHQ/s1566/cap1.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="377" data-original-width="1566" height="96" src="https://1.bp.blogspot.com/-CPoTLNw8LeE/YCRxnHjf1fI/AAAAAAAAHoQ/wog1dCNJDtgJfqX_bzBom7z8nap3C-41gCLcBGAsYHQ/w400-h96/cap1.PNG" width="400" /></a></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span><p></p><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; line-height: 107%; mso-ansi-language: ES-CO; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Si desea construir este poliedro en papel, puede encontrar los d</span><span style="text-align: center;">iagramas </span><a href="http://mars.wne.edu/~thull/phzig/phzig.html" style="text-align: center;" target="_blank">Aquí</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>
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<br />Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com2tag:blogger.com,1999:blog-4375388739861338150.post-91900485542577322562023-03-01T17:54:00.000-05:002023-03-01T17:54:41.191-05:00POLIEDROS: Construcción de un Dodecaedro<div class="separator" style="clear: both; text-align: center;"><p><span style="background-color: white; color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;">Dodecaedro</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="297" src="https://www.youtube.com/embed/sTRxTqIRWes" width="461" youtube-src-id="sTRxTqIRWes"></iframe></div><br /><span style="background-color: white; color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;"><br /></span><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="320" src="https://www.youtube.com/embed/dcxJXtxNlGU" width="489" youtube-src-id="dcxJXtxNlGU"></iframe></div><br /><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="329" src="https://www.youtube.com/embed/jsKSDLnYvAY" width="501" youtube-src-id="jsKSDLnYvAY"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO; text-align: left;">Hace parte de la familia de los sólidos regulares o poliedros Platónicos </span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt; text-align: justify;">(<a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">ver Poliedros Platónicos y Arquimedianos</a>)</span><span face="Helvetica, sans-serif" style="color: #3b170b; font-size: 11.5pt; text-align: justify;"> </span><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;">, conocidos con este nombre en honor al filósofo griego Platón, a quien se le atribuye ser el primero en estudiarlos. Es un poliedro convexo, tiene 12 caras con forma de pentágonos regulares, tiene 30 aristas y 20 vértices. Este sólido está presente en piezas arquitectónicas y de diseño, un ejemplo son las lámparas diseñadas por Gaudí ubicadas en la Cripta de la Sagrada Familia y en la Catedral de la Palma en España</span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;"><div class="separator" style="clear: both; color: black; font-family: "Times New Roman"; font-size: medium; text-align: center;"><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><a href="https://1.bp.blogspot.com/-lJf15pXwwoo/YELct7r-AeI/AAAAAAAAHws/18AJQQW8p6AFKv4554lw9YjS1fEqJ5NYQCLcBGAsYHQ/s571/1.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="473" data-original-width="571" src="https://1.bp.blogspot.com/-lJf15pXwwoo/YELct7r-AeI/AAAAAAAAHws/18AJQQW8p6AFKv4554lw9YjS1fEqJ5NYQCLcBGAsYHQ/s320/1.gif" width="320" /></a></span></div><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-BVSkwAL_ryM/YELct5NOCQI/AAAAAAAAHww/9LCDXNrLwXsO4N0nzRLiAOXufeaJaAAiACLcBGAsYHQ/s571/dode.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="473" data-original-width="571" src="https://1.bp.blogspot.com/-BVSkwAL_ryM/YELct5NOCQI/AAAAAAAAHww/9LCDXNrLwXsO4N0nzRLiAOXufeaJaAAiACLcBGAsYHQ/s320/dode.gif" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-SlvhfW_l-Ik/YELct2vdu1I/AAAAAAAAHwo/fjqM8LUxV_glnHXi5AmJ28DaWo7HkgkXACLcBGAsYHQ/s571/2.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="473" data-original-width="571" src="https://1.bp.blogspot.com/-SlvhfW_l-Ik/YELct2vdu1I/AAAAAAAAHwo/fjqM8LUxV_glnHXi5AmJ28DaWo7HkgkXACLcBGAsYHQ/s320/2.gif" width="320" /></a></div><br /></span><p style="color: black; font-family: "Times New Roman"; font-size: medium;"></p><p class="MsoNormal" style="background: white; color: black; font-family: "Times New Roman"; font-size: medium; line-height: normal; margin-bottom: 0cm;"><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">En todo poliedro regular, el número de caras más el número de vértices, es igual al número de aristas más 2. Se conoce como característica de Euler, una propiedad topológica.<o:p></o:p></span></p><p align="center" class="MsoNormal" style="background: white; color: black; font-family: "Times New Roman"; font-size: medium; line-height: normal; margin-bottom: 0cm; text-align: center;">C + V = A + 2</p><p align="center" class="MsoNormal" style="background: white; color: black; font-family: "Times New Roman"; font-size: medium; line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="color: #050505; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><o:p> </o:p></span><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;">donde: C = número de caras; V = número de vértices; A = número de aristas</span></p><p class="MsoNormal" style="background: white; color: black; font-family: "Times New Roman"; font-size: medium; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><o:p> </o:p></span><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;">El área y volumen del dodecaedro de en función de la longitud de su arista son</span></p><p class="MsoNormal" style="background: white; color: black; font-family: "Times New Roman"; font-size: medium; line-height: normal; margin-bottom: 0cm; text-align: center; vertical-align: baseline;"></p><div class="separator" style="clear: both; color: black; font-family: "Times New Roman"; font-size: medium; text-align: center;"><a href="https://1.bp.blogspot.com/-TPlfG6Go2qA/YELdOB7oi1I/AAAAAAAAHxA/Z9HH34JXpTEpsVF-fcMPhLkohCDn0_xEACLcBGAsYHQ/s1834/area%2Bdode.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="260" data-original-width="1834" height="56" src="https://1.bp.blogspot.com/-TPlfG6Go2qA/YELdOB7oi1I/AAAAAAAAHxA/Z9HH34JXpTEpsVF-fcMPhLkohCDn0_xEACLcBGAsYHQ/w400-h56/area%2Bdode.PNG" width="400" /></a></div><br style="color: black; font-family: "Times New Roman"; font-size: medium;" /><div class="separator" style="clear: both; color: black; font-family: "Times New Roman"; font-size: medium; text-align: center;"><a href="https://1.bp.blogspot.com/-QGt7l9687pA/YELdODxqLcI/AAAAAAAAHxE/swiAskoc81EgXMQDAKSxYtF3nds56K11wCLcBGAsYHQ/s1158/volu%2Bdode.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="247" data-original-width="1158" height="85" src="https://1.bp.blogspot.com/-QGt7l9687pA/YELdODxqLcI/AAAAAAAAHxE/swiAskoc81EgXMQDAKSxYtF3nds56K11wCLcBGAsYHQ/w400-h85/volu%2Bdode.PNG" width="400" /></a></div></span></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: left;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><br /></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: x-large;"><span style="background-color: transparent; font-family: Merriweather, Georgia, serif;">Si lo quieres construir en papel, esto videos te pueden ayudar</span></span></p><div class="separator" style="clear: both;"><iframe allowfullscreen="" class="BLOG_video_class" height="306" src="https://www.youtube.com/embed/iTPueayX86g" width="487" youtube-src-id="iTPueayX86g"></iframe></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: x-large;"><span style="background-color: transparent; font-family: Merriweather, Georgia, serif;"><br style="color: black; font-family: "Times New Roman"; font-size: medium;" /><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;"><br /></span></span></span></p><p></p><p></p><div class="separator" style="clear: both;"><iframe allowfullscreen="" class="BLOG_video_class" height="306" src="https://www.youtube.com/embed/1fLuzzZtNzA" width="472" youtube-src-id="1fLuzzZtNzA"></iframe></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: x-large;"><span style="background-color: transparent; font-family: Merriweather, Georgia, serif;"></span></span></p><div class="separator" style="clear: both;"><br /></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><span style="background-color: transparent; font-family: Merriweather, Georgia, serif; font-size: 16px;"><iframe allowfullscreen="" class="BLOG_video_class" height="359" src="https://www.youtube.com/embed/BKZgQFRChJ4" width="433" youtube-src-id="BKZgQFRChJ4"></iframe></span></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><iframe allowfullscreen="" class="BLOG_video_class" height="309" src="https://www.youtube.com/embed/YFEMxHL-hLs" width="477" youtube-src-id="YFEMxHL-hLs"></iframe></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: left;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><iframe allowfullscreen="" class="BLOG_video_class" height="310" src="https://www.youtube.com/embed/m0FA6B_pMvc" width="511" youtube-src-id="m0FA6B_pMvc"></iframe></span></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><iframe allowfullscreen="" class="BLOG_video_class" height="303" src="https://www.youtube.com/embed/n3mx_UdRb_Y" width="476" youtube-src-id="n3mx_UdRb_Y"></iframe></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: left;"><span style="color: #050505; font-family: "Times New Roman", serif; font-size: 13pt;"><br /></span></p></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="293" src="https://www.youtube.com/embed/64wI7jDQWUY" width="469" youtube-src-id="64wI7jDQWUY"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="324" src="https://www.youtube.com/embed/NnA1QSRbKD8" width="477" youtube-src-id="NnA1QSRbKD8"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><p style="text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="330" src="https://www.youtube.com/embed/V6U5SN-GChw" width="471" youtube-src-id="V6U5SN-GChw"></iframe></p><div><br /><span style="font-family: Merriweather, Georgia, serif;"><br /></span><div><span style="font-family: Merriweather, Georgia, serif;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/UTZFGFMiPqk" width="320" youtube-src-id="UTZFGFMiPqk"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/v4jvGR7WjuU" width="320" youtube-src-id="v4jvGR7WjuU"></iframe></div><br /><span style="font-family: Merriweather, Georgia, serif;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="348" src="https://www.youtube.com/embed/WemL4jcHwOI" width="481" youtube-src-id="WemL4jcHwOI"></iframe></div><br /><span style="font-family: Merriweather, Georgia, serif;"><br /></span><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><o:p> </o:p></span><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;"> </span></p><div class="separator" style="clear: both; text-align: center;"><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;"><iframe allowfullscreen="" class="BLOG_video_class" height="321" src="https://www.youtube.com/embed/MzeQBFay8NY" width="497" youtube-src-id="MzeQBFay8NY"></iframe></span></div><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;"><br /></span><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 13pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Esta publicación<span style="mso-spacerun: yes;"> </span>incluye imágenes
I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www
.peda.com/polypro)<o:p></o:p></span></p></div></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-11007985254228274162023-02-13T10:06:00.000-05:002023-02-13T10:06:59.122-05:00Poliedros: Construcción de un Octaedro truncado - Características<br /><div style="text-align: center;">
</div>
<h1 style="background: white; margin-bottom: 0cm; text-align: left; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: x-large; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Octaedro Truncado</span></h1><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="309" src="https://www.youtube.com/embed/lvV9xsdNgok" width="493" youtube-src-id="lvV9xsdNgok"></iframe></div><br /><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: x-large; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><br /></span></div>
<p class="MsoNormal" style="background: white; margin-bottom: 0cm; mso-line-height-alt: 12.0pt; mso-outline-level: 3; vertical-align: baseline;"><span style="font-size: medium;"><span face="Helvetica, sans-serif" style="color: #3b170b; text-align: justify;">El
octaedro truncado o</span><span style="text-align: justify;"> </span><span face="Helvetica, sans-serif" style="color: #3b170b; text-align: justify;">poliedro de Kelvin es uno de los trece poliedros ((<a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">ver Poliedros Platónicos y Arquimedianos</a>)) de Arquímedes,
también conocidos como poliedro semirregulares o poliedros arquimedianos. Se forma al truncar
(cortar) los vértices de un octaedro, se eliminan seis pirámides cuadradas, una
en cada vértice. Dichas pirámides tienen una longitud de base y una longitud
lateral, formando triángulos equiláteros. De este truncamiento se forman 14
caras (8 hexágonos regulares y 6 cuadrados), tiene 36 aristas y 24 vértices.</span></span></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> <br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-uwMbMf8DdRo/YCVnvUXouSI/AAAAAAAAHoo/nvBQrOq-rmUL1GOqq5Psnsk8GHmsHcvCwCLcBGAsYHQ/s1024/1024px-Truncated_Octahedron_with_Construction.svg.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1024" data-original-width="1024" height="320" src="https://1.bp.blogspot.com/-uwMbMf8DdRo/YCVnvUXouSI/AAAAAAAAHoo/nvBQrOq-rmUL1GOqq5Psnsk8GHmsHcvCwCLcBGAsYHQ/s320/1024px-Truncated_Octahedron_with_Construction.svg.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-MObXNz4iEKU/YCVnvRCPlCI/AAAAAAAAHok/3loNnCfic9YGmAKqVRZTWUsMe2F6JRx9ACLcBGAsYHQ/s657/octaedro%2Btruncado..gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="585" data-original-width="657" src="https://1.bp.blogspot.com/-MObXNz4iEKU/YCVnvRCPlCI/AAAAAAAAHok/3loNnCfic9YGmAKqVRZTWUsMe2F6JRx9ACLcBGAsYHQ/s320/octaedro%2Btruncado..gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-tdnzYXFI5Fc/YCVnvaZcu7I/AAAAAAAAHog/7kX4uPmqkCoXLnVtUb4A0oCLZzUuIQO9wCLcBGAsYHQ/s657/octaedro%2Btruncado.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="585" data-original-width="657" src="https://1.bp.blogspot.com/-tdnzYXFI5Fc/YCVnvaZcu7I/AAAAAAAAHog/7kX4uPmqkCoXLnVtUb4A0oCLZzUuIQO9wCLcBGAsYHQ/s320/octaedro%2Btruncado.gif" width="320" /></a></div><br /><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: justify; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: medium; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Es
el único poliedro semirregular que puede llenar completamente el espacio por
repetición de sí mismo. Es decir, que uniendo octaedros truncados del mismo
tamaño podemos llenar el espacio sin dejar huecos entre ellos. <o:p></o:p></span></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="font-size: medium;"><span face=""Helvetica",sans-serif" style="color: #3b170b; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span><span face="Helvetica, sans-serif" style="color: #3b170b;">El área y volumen del octaedro truncado en función de la longitud de la arista son:</span></span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-gxan-Hj0q6A/YCVqXfArQXI/AAAAAAAAHo8/qSZWCMVE6xIlnbxizy3ny-wynAzmz4JZQCLcBGAsYHQ/s1704/area%2Boctaedro%2Btruncado.PNG" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img border="0" data-original-height="365" data-original-width="1704" height="86" src="https://1.bp.blogspot.com/-gxan-Hj0q6A/YCVqXfArQXI/AAAAAAAAHo8/qSZWCMVE6xIlnbxizy3ny-wynAzmz4JZQCLcBGAsYHQ/w400-h86/area%2Boctaedro%2Btruncado.PNG" width="400" /></span></a></div><span style="font-size: medium;"><br /><span face="Helvetica, sans-serif" style="color: #3b170b;">Si quieres construirlo en papel, puedes encontra el video tutorial</span><span style="background-color: transparent; text-align: center;"> </span><a href="http://www.youtube.com/watch?v=wD5q83k3tOE&feature=plcp" style="background-color: transparent; text-align: center;">AQUÍ</a></span><p></p>
<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span face=""Helvetica",sans-serif" style="color: #3b170b; font-size: 11.5pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"> </span></p>
<div style="text-align: center;">
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<br /></div><div style="text-align: left;"><span face="Helvetica, sans-serif" style="background-color: white; color: #3b170b; font-size: medium;">Esta publicación incluye imágenes I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www .peda.com/polypro)</span></div>
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Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-71162241529544430112023-02-02T07:57:00.001-05:002023-02-07T08:48:50.864-05:00Animales en origami - Animales de Papel<p> </p><p style="text-align: center;">CISNE</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="244" src="https://www.youtube.com/embed/BE_T8FVkqk8" width="380" youtube-src-id="BE_T8FVkqk8"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">RANA</div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="324" src="https://www.youtube.com/embed/bZMOT038A9U" width="390" youtube-src-id="bZMOT038A9U"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">CONEJO</div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="312" src="https://www.youtube.com/embed/7ybrZFn5v04" width="375" youtube-src-id="7ybrZFn5v04"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">GRULLA</div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="304" src="https://www.youtube.com/embed/RMdLXjfTEoc" width="366" youtube-src-id="RMdLXjfTEoc"></iframe></div><br /><p><br /></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-9031429091695103592023-01-25T19:48:00.002-05:002023-01-25T19:48:27.629-05:00Bases del Origami<span style="font-size: medium;">Cuando realizamos origami en el proceso de plegado se presenta con regularidad que los primeros pasos son iguales, esto llevó a establecer algunas bases que permiten continuar la elaboración de diferentes modelos.</span><div style="text-align: left;"><span style="font-size: medium;"><br /></span></div><div style="text-align: left;"><span style="font-size: medium;">En esta publicación presento videos con las bases más comune</span>s.</div><div style="text-align: left;"><span style="font-size: x-large;"><br /></span></div><div style="text-align: left;"><span style="font-size: x-large;">Base Pez</span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/ovF496tWdgY" width="443" youtube-src-id="ovF496tWdgY"></iframe></div><span style="font-size: x-large;"><div><span style="font-size: x-large;"><br /></span></div>Base Bomba de agua</span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="297" src="https://www.youtube.com/embed/p9DC7pintaE" width="424" youtube-src-id="p9DC7pintaE"></iframe></div><span style="font-size: x-large;">Base Preliminar</span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="283" src="https://www.youtube.com/embed/OwgvPUGBdnw" width="418" youtube-src-id="OwgvPUGBdnw"></iframe></div><span style="font-size: x-large;">Base Molino</span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="306" src="https://www.youtube.com/embed/kSivf4CccZQ" width="438" youtube-src-id="kSivf4CccZQ"></iframe></div><span style="font-size: x-large;">Base Pájaro</span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="308" src="https://www.youtube.com/embed/eWLxLlJjedU" width="465" youtube-src-id="eWLxLlJjedU"></iframe></div><span style="font-size: x-large;">Base Rana</span></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="301" src="https://www.youtube.com/embed/xQGkP6ETlaU" width="459" youtube-src-id="xQGkP6ETlaU"></iframe></div><br /><span style="font-size: x-large;"><br /></span></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-7102194959024571352023-01-22T20:27:00.000-05:002023-01-22T20:27:10.421-05:00Poliedros: Tetraedro truncado<p> </p><h1><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Tetraedro Truncado<o:p></o:p></span></h1><div style="text-align: left;"><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;"><iframe allowfullscreen="" class="BLOG_video_class" height="331" src="https://www.youtube.com/embed/UA0DChAPOAw" width="490" youtube-src-id="UA0DChAPOAw"></iframe></span></div>
<p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #050505; font-size: 13pt;"><br /></span></p><p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #050505; font-size: 13pt;">El Tetraedro truncado hace parte de la familia de los sólidos
semirregulares o poliedros arquimedianos, c</span><span style="color: #202122; font-size: 13pt;">onocidos con este nombre en honor al matemático Arquímedes quien
describió extensamente estos cuerpos. </span><span style="color: #050505; font-size: 13pt;">Es el poliedro menor de la familia de los sólidos de Arquímedes.
Es un poliedro convexo, que se obtiene </span><span style="color: #3b170b;">truncando
(cortando) los vértices del tetraedro a un tercio de la longitud de la arista. Se
eliminan tres tetraedros, uno en cada vértice. Con esto</span><span style="color: #050505; font-size: 13pt;"> resultan 8 caras: 4 del tetraedro
original que se convierten de triangulares a hexagonales y 4 nuevas que
resultan de los vértices, en este caso triangulares. <o:p></o:p></span></p>
<p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #050505; font-size: 13pt;"><o:p> </o:p></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-W8As5Bp3W74/YbQRfutpHJI/AAAAAAAAJNI/N1NrC_DCIHUB9MZExjWBYitlLWbomaEzACNcBGAsYHQ/s516/Tetraedro%2Btruncado.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="487" data-original-width="516" height="302" src="https://1.bp.blogspot.com/-W8As5Bp3W74/YbQRfutpHJI/AAAAAAAAJNI/N1NrC_DCIHUB9MZExjWBYitlLWbomaEzACNcBGAsYHQ/s320/Tetraedro%2Btruncado.gif" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-U1ZjPb2CuFY/YbQRfqm5lTI/AAAAAAAAJNE/jJE2sIcuwk894tTNcxHP3gwjNp9G5nCugCNcBGAsYHQ/s516/Tetraedro%2Btruncado%2B2.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="487" data-original-width="516" height="302" src="https://1.bp.blogspot.com/-U1ZjPb2CuFY/YbQRfqm5lTI/AAAAAAAAJNE/jJE2sIcuwk894tTNcxHP3gwjNp9G5nCugCNcBGAsYHQ/s320/Tetraedro%2Btruncado%2B2.gif" width="320" /></a></div><br /><p></p>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTable15Grid4Accent2" style="border-collapse: collapse; border: none; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 280px;">
<tbody><tr style="mso-yfti-firstrow: yes; mso-yfti-irow: -1; mso-yfti-lastfirstrow: yes;">
<td colspan="2" style="background: rgb(237, 125, 49); border: 1pt solid rgb(237, 125, 49); mso-background-themecolor: accent2; mso-border-alt: solid #ED7D31 .5pt; mso-border-themecolor: accent2; padding: 0cm 5.4pt; width: 210pt;" valign="top" width="280">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 5; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 16pt;">Tetraedro<span style="color: black; mso-color-alt: windowtext;"> truncado</span><o:p></o:p></span></b></p>
</td>
</tr>
<tr style="mso-yfti-irow: 0;">
<td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 68; text-align: center;"><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;">Caras</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 64; text-align: center;"><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;">8</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Configuración
de las caras<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">4 hexágonos<o:p></o:p></span></b></p>
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">4 triángulos equiláteros<o:p></o:p></span></b></p>
</td>
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<tr style="mso-yfti-irow: 2;">
<td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 68; text-align: center;"><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;">Aristas</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 64; text-align: center;"><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;">18</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Vértices<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">12<o:p></o:p></span></b></p>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 68; text-align: center;"><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;">Configuración de vértices</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 0cm; mso-yfti-cnfc: 64; text-align: center;"><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;">Uniforme de orden 3<br />
1 Triángulo</span></b><b><span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-color-alt: windowtext;"><br />
2 Hexágonos</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
</tr>
</tbody></table>
</div>
<p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #050505; font-size: 13pt;"><o:p> </o:p></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Ymrdj-jLxH4/YbQRmQVSirI/AAAAAAAAJNM/pjyt5APSh289ERiGeE8gFR3zyGn2ao-WwCNcBGAsYHQ/s516/Tetraedro%2Btruncado%2B3.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="487" data-original-width="516" height="302" src="https://1.bp.blogspot.com/-Ymrdj-jLxH4/YbQRmQVSirI/AAAAAAAAJNM/pjyt5APSh289ERiGeE8gFR3zyGn2ao-WwCNcBGAsYHQ/s320/Tetraedro%2Btruncado%2B3.gif" width="320" /></a></div><br /><p></p>
<p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #050505; font-size: 13pt;"><o:p> </o:p></span><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;">El área y volumen del dodecaedro de en función de la longitud de su
arista son</span></p><p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt; text-align: left;"><br /></span></p><p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-ZPeyOn3WK-E/YbQR4UaHEEI/AAAAAAAAJNk/QcfkFJHhRTgFfo04WPPcl0x1NpbBEKhhgCNcBGAsYHQ/s752/1.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="136" data-original-width="752" height="73" src="https://1.bp.blogspot.com/-ZPeyOn3WK-E/YbQR4UaHEEI/AAAAAAAAJNk/QcfkFJHhRTgFfo04WPPcl0x1NpbBEKhhgCNcBGAsYHQ/w400-h73/1.PNG" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-dmdaHVy1UwU/YbQR5xe8fKI/AAAAAAAAJNo/eOeUJ1tbtUsy81aG5fZqFEIUuG0cyKDzACNcBGAsYHQ/s782/2.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="204" data-original-width="782" height="104" src="https://1.bp.blogspot.com/-dmdaHVy1UwU/YbQR5xe8fKI/AAAAAAAAJNo/eOeUJ1tbtUsy81aG5fZqFEIUuG0cyKDzACNcBGAsYHQ/w400-h104/2.PNG" width="400" /></a></div><p></p><p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><span style="color: #3b170b; font-family: Merriweather, Georgia, serif; text-align: start;">Si quieres construirlo en papel, puedes encontrar el video tutorial</span><span style="background-color: transparent; font-family: Merriweather, Georgia, serif; text-align: center;"> </span></p><p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="331" src="https://www.youtube.com/embed/UA0DChAPOAw" width="490" youtube-src-id="UA0DChAPOAw"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;">Esta publicación</span><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;"> </span><span style="color: #3b170b; font-family: "Times New Roman", serif; font-size: 13pt;">incluye imágenes
I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www
.peda.com/polypro)</span><p></p><p style="background: white; margin-bottom: 6.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm; text-align: justify;"><br /></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-87197535424066083402022-12-09T11:12:00.000-05:002022-12-09T11:12:04.013-05:00Método abreviado de multiplicación por 11<p> Esta es una manera sencilla de multiplicar números de dos cifras por el número 11</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzCdGWd9SB_OQDcjzq1yTsAPpSp11_uO-uyaF87z49l-LOYlw6iGzPyCBHNDgcvsNVwLse-QUh0qcGAJfG4K4zyfzodhHGJIV2CXpEMWyX79TY4fJzYyVqBXGx79VWUftV-M5_B4hOGDeo5QMaUuGozF-8FS1-Ktgk1wcbdRoo9Ww80Qdb28CqSg5B/s1649/Multiplicaci%C3%B3n%20por%2011.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1649" data-original-width="908" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzCdGWd9SB_OQDcjzq1yTsAPpSp11_uO-uyaF87z49l-LOYlw6iGzPyCBHNDgcvsNVwLse-QUh0qcGAJfG4K4zyfzodhHGJIV2CXpEMWyX79TY4fJzYyVqBXGx79VWUftV-M5_B4hOGDeo5QMaUuGozF-8FS1-Ktgk1wcbdRoo9Ww80Qdb28CqSg5B/w220-h400/Multiplicaci%C3%B3n%20por%2011.jpg" width="220" /></a></div><br /><p></p><p>En este video te explico de manera sencilla como realizar la multiplicación por el número 11</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="339" src="https://www.youtube.com/embed/OWHNJfr0teI" width="457" youtube-src-id="OWHNJfr0teI"></iframe></div><br /><p><br /></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-74258843482235597712022-10-26T10:01:00.000-05:002022-10-26T10:01:58.518-05:00Poliedros Platónicos y Arquimedianos<p> </p><h1 style="line-height: 150%; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;"><o:p> <br /><div style="text-align: center;"><b><span lang="ES" style="line-height: 150%;"><span style="font-size: medium;"> POLIEDROS</span></span></b></div></o:p></span></b></h1>
<h3 style="line-height: 150%; margin-left: 18pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Poliedros
Regulares (Platónicos)</span></b></h3>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; text-transform: uppercase;"><o:p> </o:p></span></b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">En geometría los sólidos</span><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> </span><span style="font-family: "Times New Roman", serif; font-size: 12pt;">de caras planas reciben el nombre de
“poliedros” (de las palabras griegas </span><i style="font-family: "Times New Roman", serif; font-size: 12pt;">polys</i><span style="font-family: "Times New Roman", serif; font-size: 12pt; text-transform: uppercase;">:</span><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> “múltiples”, y</span><i style="font-family: "Times New Roman", serif; font-size: 12pt;"> hedra</i><span style="font-family: "Times New Roman", serif; font-size: 12pt; text-transform: uppercase;">:</span><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> “cara”).
Los poliedros cuyas caras son polígonos regulares, se llaman </span><i style="font-family: "Times New Roman", serif; font-size: 12pt;">poliedros
regulares</i><span style="font-family: "Times New Roman", serif; font-size: 12pt;">, los cuales</span><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> </span><span style="font-family: "Times New Roman", serif; font-size: 12pt;">son cinco.</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-4JpGVhu5L5k/YBVdyo13o1I/AAAAAAAAHjc/1AhW1VSdT6kIdcUVFziiGld1c9EHKEgdQCLcBGAsYHQ/s497/1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="117" data-original-width="497" height="94" src="https://1.bp.blogspot.com/-4JpGVhu5L5k/YBVdyo13o1I/AAAAAAAAHjc/1AhW1VSdT6kIdcUVFziiGld1c9EHKEgdQCLcBGAsYHQ/w400-h94/1.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="295" src="https://www.youtube.com/embed/Z9h157w-dZo" width="516" youtube-src-id="Z9h157w-dZo"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="304" src="https://www.youtube.com/embed/n7OKE3uQ6wM" width="480" youtube-src-id="n7OKE3uQ6wM"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold; text-align: justify; text-transform: uppercase;"><o:p> </o:p></span><span style="font-family: "Times New Roman", serif; font-size: 12pt; text-align: justify;">Para mostrar porqué</span><span style="font-family: "Times New Roman", serif; font-size: 12pt; mso-spacerun: yes; text-align: justify;">
</span><span style="font-family: "Times New Roman", serif; font-size: 12pt; text-align: justify;">son cinco – y no más – se suele razonar del modo siguiente:</span></div>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold; text-transform: uppercase;"><o:p> </o:p></span><span lang="ES" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 150%; text-indent: -25.5pt; text-transform: uppercase;">(1)<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><span lang="ES" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 150%; text-indent: -25.5pt;">Cada vértice debe ser común por lo menos a tres
caras para que se forme un sólido.<span style="text-transform: uppercase;"> </span></span><span lang="ES" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 150%; text-indent: -25.5pt; text-transform: uppercase;">(2)<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><span lang="ES" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 150%; text-indent: -25.5pt;">La suma de los ángulos interiores de las caras que
se encuentren en cada vértice debe ser menor que 360°, de manera que la figura
se cierre, que no sea plana.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 43.5pt; mso-list: l0 level1 lfo1; tab-stops: list 43.5pt; text-align: justify; text-indent: -25.5pt;"><!--[if !supportLists]--><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold; text-transform: uppercase;"><span style="mso-list: Ignore;">(3)<span style="font: 7pt "Times New Roman";"> </span></span></span><!--[endif]--><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold;">Dado que cada ángulo interior de un triángulo
equilátero mide 60°, tomando en cuenta lo señalado en los puntos (1) y (2), en
un vértice podrían concurrir tres, cuatro o cinco de ellos. Esos son los casos
del tetraedro, el octaedro y el icosaedro, respectivamente. Cada ángulo
interior de<span style="mso-spacerun: yes;"> </span>un cuadrado mide 90°, de
modo que solo podemos hacer coincidir tres de ellos en cada vértice. Ese es el
caso del hexaedro (cubo). Los ángulos interiores de un pentágono regular miden
108°. Poniendo tres de ellos en cada vértice se obtiene un dodecaedro. Con los
siguientes polígonos ya no es posible formar poliedros regulares: los ángulos
interiores de un hexágono miden 120° y no es posible poner tres juntos sin
llegar al límite de 360°; los ángulos interiores de los siguientes son aún
mayores. <span style="text-transform: uppercase;"><o:p></o:p></span></span></p>
<p class="MsoNormal" style="line-height: 150%; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold; text-transform: uppercase;"><o:p> </o:p></span><span style="font-family: "Times New Roman", serif; font-size: 12pt;">En el siguiente cuadro</span><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> </span><span style="font-family: "Times New Roman", serif; font-size: 12pt;">se presentan sus nombres y características.</span></p>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGridLight" style="border-collapse: collapse; border: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; width: 100%px;">
<tbody><tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-themecolor: background1; mso-border-themeshade: 191; padding: 0cm 5.4pt; width: 16.52%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Poliedro
Regular<o:p></o:p></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">Tetraedro Regular<o:p></o:p></span></p>
</td>
<td style="border-left: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; padding: 0cm 5.4pt; width: 16.62%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">Hexaedro Regular<o:p></o:p></span></p>
</td>
<td style="border-left: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">Octaedro Regular<o:p></o:p></span></p>
</td>
<td style="border-left: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; padding: 0cm 5.4pt; width: 16.9%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">Dodecaedro Regular<o:p></o:p></span></p>
</td>
<td style="border-left: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">Icosaedro Regular<o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.52%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Caras<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">4 triángulos Equiláteros<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.62%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">6 cuadrados<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">8 triángulos Equiláteros<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.9%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">12 pentágonos Regulares<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">20 triángulos Equiláteros<o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.52%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Vértices<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">4<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.62%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">8<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">6<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.9%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">20<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">12<o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.52%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Aristas<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">6<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.62%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">12<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">12<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.9%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">30<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">30<o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: 1pt solid rgb(191, 191, 191); mso-border-alt: solid #BFBFBF .5pt; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.52%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Aristas
Por Vértice<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">3<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.62%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">3<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">4<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.9%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">3<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid rgb(191, 191, 191); border-left: none; border-right: 1pt solid rgb(191, 191, 191); border-top: none; mso-border-alt: solid #BFBFBF .5pt; mso-border-bottom-themecolor: background1; mso-border-bottom-themeshade: 191; mso-border-left-alt: solid #BFBFBF .5pt; mso-border-left-themecolor: background1; mso-border-left-themeshade: 191; mso-border-right-themecolor: background1; mso-border-right-themeshade: 191; mso-border-themecolor: background1; mso-border-themeshade: 191; mso-border-top-alt: solid #BFBFBF .5pt; mso-border-top-themecolor: background1; mso-border-top-themeshade: 191; padding: 0cm 5.4pt; width: 16.64%;" valign="top" width="16%">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%; mso-bidi-font-weight: bold;">5<o:p></o:p></span></p>
</td>
</tr>
</tbody></table>
<h3 style="line-height: 150%; margin-left: 18pt; text-align: justify;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Construcción de cubo</span></b></h3><div><b><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/9MD0RhXxXR8" width="320" youtube-src-id="9MD0RhXxXR8"></iframe></div><div><b><br /></b></div>Construcción de Tetraedro</b></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/0mZVFK9rFf0" width="320" youtube-src-id="0mZVFK9rFf0"></iframe></div><br /><b>Construcción de Octaedro</b></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/-Fuf91fwZM4" width="320" youtube-src-id="-Fuf91fwZM4"></iframe></div><br /><b>Construcción de Dodecaedro</b></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/WemL4jcHwOI" width="320" youtube-src-id="WemL4jcHwOI"></iframe></div><br /><b>Construcción de Icosaedro</b></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/HSC00CjOl1U" width="320" youtube-src-id="HSC00CjOl1U"></iframe></div><br /><b><br /><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;"><br /></span></b></div><h3 style="line-height: 150%; margin-left: 18pt; text-align: justify;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Poliedros
Semirregulares (Arquimedianos)</span></b></h3>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; text-transform: uppercase;"><o:p> </o:p></span></b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Los poliedros </span><b style="font-family: "Times New Roman", serif; font-size: 12pt;">arquimedianos<span style="text-transform: uppercase;"> </span></b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">o</span><b style="font-family: "Times New Roman", serif; font-size: 12pt;"> semirregulares</b><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> son
sólidos que tienen todas las caras (polígonos) regulares y en cada vértice
concurre el mismo número de aristas, pero no todas las caras son iguales, por
tener cada uno más de un tipo de polígono</span><span style="font-family: "Times New Roman", serif; font-size: 12pt; text-transform: uppercase;">.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><a href="https://1.bp.blogspot.com/-7e6h3r7zofc/YBVegyU26_I/AAAAAAAAHjk/372wUOrYIt8zEx2x1xxj6Wq5dTE7JM-8wCLcBGAsYHQ/s690/2.jpg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="387" data-original-width="690" height="224" src="https://1.bp.blogspot.com/-7e6h3r7zofc/YBVegyU26_I/AAAAAAAAHjk/372wUOrYIt8zEx2x1xxj6Wq5dTE7JM-8wCLcBGAsYHQ/w400-h224/2.jpg" width="400" /></a></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold;">Su nombre se debe a que fue Arquímedes el que los
describió por primera vez. Arquímedes describió estos poliedros indicando el
número de polígonos que concurren en cada vértice y el número de lados de estos
polígonos. <span style="text-transform: uppercase;"><o:p></o:p></span></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold;">Kepler fue quien dio nombre a estos poliedros y
probó que hay trece poliedros arquimedianos, además de los prismas y
antiprismas de caras regulares, pero en 1904 Sommerville (1879-1934) describió
el pseudorrombicuboctaedro que es el<span style="mso-spacerun: yes;">
</span>poliedro semirregular número 14.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold;">Algunos de estos poliedros arquimedianos se utilizan
como elementos decorativos en farolas y otros adornos. Hasta hace pocos años
los balones de fútbol estaban hechos con uno de estos poliedros, el formado con
hexágonos y pentágonos (icosaedro truncado), aunque no siempre había sido así;
parece que los griegos utilizaban dodecaedros para la construcción de sus
balones. Ahora el balón oficial también corresponde a un poliedro arquimediano,
el pequeño rombicosidodecaedro que está formado por 20 triángulos, 30 cuadrados
y 12 pentágonos<span style="text-transform: uppercase;">.</span></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold; text-transform: uppercase;">E</span><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-bidi-font-weight: bold;">n la siguiente tabla se presentan sus nombres y sus
características</span></p>
<div align="center"><div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt;">
<tbody><tr>
<td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Nombre</span></b><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;"><o:p></o:p></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Caras</span></b><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;"><o:p></o:p></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Vértices</span></b><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;"><o:p></o:p></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Aristas</span></b><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;"><o:p></o:p></span></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Aristas
por vértice<o:p></o:p></span></b></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Tetraedro
truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">4 triángulos, 4
hexágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">12<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">18<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Cuboctaedro<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">8 triángulos, 6
cuadrados<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">12<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">24<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">4<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Cubo
truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">8 triángulos, 6
octágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">24<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">36<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Octaedro
truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">6 cuadrados, 8
hexágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">24<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">36<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Pequeño
rombicuboctaedro<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">8 triángulos, 18
cuadrados<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">24<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">48<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">4<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Pseudorrombicuboctaedro<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">8 triángulos,18
cuadrados<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">24<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">48<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">4<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Gran
rombicuboctaedro o cuboctaedro truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">12 cuadrados, 8
hexágonos, 6 octágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">48<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">72<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Cubo
chato<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">32 triángulos, 6
cuadrados<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">24<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">60<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">5<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Icosidodecaedro<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">20 triángulos, 12
pentágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">30<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">60<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">4<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Dodecaedro
truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">20 triángulos, 12
decágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">60<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">90<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Icosaedro
truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">12 pentágonos, 20
hexágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">60<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">90<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Pequeño
rombicosidodecaedro<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">20 triángulos, 30
cuadrados, 12 pentágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">60<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">120<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">4<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Gran
rombicosidodecaedro o icosidodecaedro truncado<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">30 cuadrados, 20
hexágonos, 12 decágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">120<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">180<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">3<o:p></o:p></span></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 126.3pt;" width="168">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">Dodecaedro
chato<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">80 triángulos, 12
pentágonos<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">60<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt;">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">150<o:p></o:p></span></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 59.2pt;" width="79">
<p align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 11pt; line-height: 150%;">5<o:p></o:p></span></p>
</td>
</tr>
</tbody></table>
</div></div><h3 style="text-align: left;"><span style="text-align: justify;"><span lang="ES" style="line-height: 150%;">Relaciones Geométricas Entre Los Poliedros Platónicos Y Los Poliedros
Arquimedianos</span></span></h3>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Para
obtener cada uno de los poliedros semirregulares debemos realizar una serie de
operaciones, partiendo de los poliedros regulares, dichas operaciones son:</span><span lang="ES" style="line-height: 150%;"><span style="font-size: xx-small;"> </span></span><span lang="ES" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 150%; text-indent: -25.5pt;">Truncamientos y un</span><span lang="ES" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 150%; text-indent: -25.5pt;">ión de los puntos
medios de las aristas</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">En
los siguientes mapas conceptuales se presenta la relación entre los poliedros
regulares y los poliedros semirregulares.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;"><o:p> <a href="https://1.bp.blogspot.com/-FdK-uBIXR0o/YBVfVXn-kyI/AAAAAAAAHjw/fFPVzV1ELSMc6wKyz9k24Gfal4o-acULgCLcBGAsYHQ/s1050/3.PNG" style="font-size: 12pt; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="265" data-original-width="1050" height="101" src="https://1.bp.blogspot.com/-FdK-uBIXR0o/YBVfVXn-kyI/AAAAAAAAHjw/fFPVzV1ELSMc6wKyz9k24Gfal4o-acULgCLcBGAsYHQ/w400-h101/3.PNG" width="400" /></a></o:p></span><br /></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Obtención
del tetraedro truncado a partir del tetraedro</span></p><p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-AtJVP22B8_s/YBVfmQPIEkI/AAAAAAAAHj4/jyJ47L2MuzULxK3tUTS-aYZPsQZ--qEmQCLcBGAsYHQ/s337/4.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="327" data-original-width="337" height="194" src="https://1.bp.blogspot.com/-AtJVP22B8_s/YBVfmQPIEkI/AAAAAAAAHj4/jyJ47L2MuzULxK3tUTS-aYZPsQZ--qEmQCLcBGAsYHQ/w200-h194/4.PNG" width="200" /></a></div><p></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Obtención
del cubo truncado, cuboctaedro, gran rombicuboctaedro, pequeño rombicuboctaedro
y pseudorrombicuboctaedro, a partir del hexaedro. <o:p></o:p></span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-oePn7kXMJHU/YBVgEOKrs6I/AAAAAAAAHkA/InfB7JFL15Y-hw8qL6cM45SbnN2rRhM8wCLcBGAsYHQ/s872/5.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="673" data-original-width="872" height="309" src="https://1.bp.blogspot.com/-oePn7kXMJHU/YBVgEOKrs6I/AAAAAAAAHkA/InfB7JFL15Y-hw8qL6cM45SbnN2rRhM8wCLcBGAsYHQ/w400-h309/5.PNG" width="400" /></a></div>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Obtención
del octaedro truncado, cuboctaedro, gran rombicuboctaedro, pequeño
rombicuboctaedro y pseudorrombicuboctaedro, a partir del octaedro.</span></p>
<p align="center" class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: center;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;"><o:p></o:p></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-b8uD1CJ_qYI/YBVgcv28KWI/AAAAAAAAHkI/I-keSgOchv4QsVukm3zLo0x8iYtb-r-mgCLcBGAsYHQ/s940/6.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="771" data-original-width="940" height="328" src="https://1.bp.blogspot.com/-b8uD1CJ_qYI/YBVgcv28KWI/AAAAAAAAHkI/I-keSgOchv4QsVukm3zLo0x8iYtb-r-mgCLcBGAsYHQ/w400-h328/6.PNG" width="400" /></a><span style="font-size: 12pt;"> </span></div><p></p>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Obtención
del dodecaedro truncado, cubo chato, icosidodecaedro, gran rombicosidodecaedro
y pequeño rombicosidodecaedro a partir del dodecaedro.<o:p></o:p></span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-rd8PXCi-LE0/YBVgwGhS0hI/AAAAAAAAHkQ/tMHdxxOd3cQXFqEZLuTJ_Rq4ooQWMkDNwCLcBGAsYHQ/s1152/7.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="601" data-original-width="1152" height="209" src="https://1.bp.blogspot.com/-rd8PXCi-LE0/YBVgwGhS0hI/AAAAAAAAHkQ/tMHdxxOd3cQXFqEZLuTJ_Rq4ooQWMkDNwCLcBGAsYHQ/w400-h209/7.PNG" width="400" /></a></div>
<p class="MsoNormal" style="line-height: 150%; margin-left: 18pt; text-align: justify;"><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">Obtención
del icosaedro truncado, dodecaedro chato, icosidodecaedro, gran
rombicosidodecaedro y pequeño rombicosidodecaedro a partir del icosaedro.<o:p></o:p></span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-6Cx_Pcy-uAc/YBVg95jGXPI/AAAAAAAAHkU/BxAWW0fsNJgV_yCfWWPKxG_Dosw233w8ACLcBGAsYHQ/s1282/8.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="746" data-original-width="1282" height="233" src="https://1.bp.blogspot.com/-6Cx_Pcy-uAc/YBVg95jGXPI/AAAAAAAAHkU/BxAWW0fsNJgV_yCfWWPKxG_Dosw233w8ACLcBGAsYHQ/w400-h233/8.PNG" width="400" /></a></div>
<p class="MsoNormal"><span lang="ES" style="font-family: "Times New Roman",serif;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="ES" style="font-family: "Times New Roman",serif;">REFERENCIAS:</span></p>
<p class="MsoListParagraph" style="line-height: 150%; mso-list: l1 level1 lfo3; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-ansi-language: ES-MX;"><span style="mso-list: Ignore;">1.<span style="font: 7pt "Times New Roman";"> </span></span></span><!--[endif]--><span lang="ES-MX" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-ansi-language: ES-MX;">EXTREMIANA, J. Ignacio, HERNÁNDEZ, Javier y RIVAS, M.
Teresa: Cuerpos e Ideas Platónicas.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; text-indent: 35.4pt;"><span lang="ES" style="font-family: "Times New Roman",serif;"><a href="https://www.unirioja.es/cu/luhernan/Divul/POLIEDROS/cuerpos.html"><span color="windowtext" style="text-decoration: none; text-underline: none;">https://www.unirioja.es/cu/luhernan/Divul/POLIEDROS/cuerpos.html</span></a><o:p></o:p></span></p>
<p class="MsoListParagraphCxSpFirst" style="line-height: 150%; mso-list: l1 level1 lfo3; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES" style="font-family: "Times New Roman",serif;"><span style="mso-list: Ignore;">2.<span style="font: 7pt "Times New Roman";"> </span></span></span><!--[endif]--><span lang="ES" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%;">GUILLÉN,
Gregoria: El mundo de los poliedros. Sintesis.1995</span><span lang="ES" style="font-family: "Times New Roman",serif;"><o:p></o:p></span></p>
<p class="MsoListParagraphCxSpLast" style="line-height: 150%; mso-list: l1 level1 lfo3; text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-ansi-language: ES-MX;"><span style="mso-list: Ignore;">3.<span style="font: 7pt "Times New Roman";"> </span></span></span><!--[endif]--><span lang="ES" style="font-family: "Times New Roman",serif;">NIÑO, Jaime: Monografía: </span><span lang="ES-MX" style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 150%; mso-ansi-language: ES-MX;">una propuesta para<span style="mso-spacerun: yes;">
</span>la<span style="mso-spacerun: yes;"> </span>construcción de los poliedros
platónicos y de los<span style="mso-spacerun: yes;"> </span>arquimedianos
mediante el origami y el estudio matemático de sus características. 2004<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left: 18pt;"><span lang="ES" style="font-family: "Times New Roman",serif;"><o:p> </o:p></span></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-47852769645793759632022-09-26T10:29:00.004-05:002022-09-26T10:49:30.217-05:00Poliedros: Dodecaedro Rómbico o Rombododecaedro<p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="color: red; font-family: "Times New Roman",serif; font-size: 20pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Dodecaedro Rómbico o Rombododecaedro</span></p><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="333" src="https://www.youtube.com/embed/KvqH1BfkR-I" width="423" youtube-src-id="KvqH1BfkR-I"></iframe></div><br /><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm;"><span style="background-color: transparent; color: #050505; font-family: "Times New Roman", serif; font-size: 13pt; line-height: 107%;">El rombododecaedro hace parte de la
familia de los sólidos de Catalan, c</span><span style="background-color: transparent; color: #202122; font-family: "Times New Roman", serif; font-size: 13pt; line-height: 107%;">onocidos
con este nombre en honor al matemático Eugene Charles catalán, esta familia de poliedros
se generan con el poliedro dual de los <a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">sólidos semirregulares</a> (sólidos de Arquímedes),
el dual del rombododecaedro es el <a href="http://origamiymatematicas.blogspot.com/2022/01/poliedro-cuboctaedro.html" target="_blank">cuboctaedro</a>. Es un poliedro convexo de caras
y aristas uniformes, este sólido puede llenar el espacio cuando se reúnen varios
de ellos, tiene 12 caras en forma de rombo</span><span style="background-color: transparent; font-family: "Times New Roman", serif; font-size: 12pt;"> </span></p>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTable15Grid4Accent2" style="border-collapse: collapse; border: none; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 280px;">
<tbody><tr>
<td colspan="2" style="background: rgb(237, 125, 49); border: 1pt solid rgb(237, 125, 49); mso-background-themecolor: accent2; mso-border-alt: solid #ED7D31 .5pt; mso-border-themecolor: accent2; padding: 0cm 5.4pt; width: 210pt;" valign="top" width="280">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 5; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 16pt;">Rombododecaedro</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 16pt;"><o:p></o:p></span></b></p>
</td>
</tr>
<tr>
<td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 68; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Caras</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 64; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">12</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Aristas<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">24<o:p></o:p></span></b></p>
</td>
</tr>
<tr>
<td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 68; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Vértices</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 64; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">14</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Configuración
de vértices<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">6 de orden 4<o:p></o:p></span></b></p>
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">8 de orden 3<o:p></o:p></span></b></p>
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">En serie: 3, 4,
3, 4<o:p></o:p></span></b></p>
</td>
</tr>
</tbody></table>
</div>
<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHNHHpDXREKANSMTD5AE3MKLSICTbRR1MdQ6XKZJObBQlvRbyunXXEVnB1NcHH0YAdK3vC9KyGml5eA_P0T3FN-yX8dedcGu1NjcmVHL7tvwZVD39ymcb0Ih4OWPM4vW4J8ppbL2KtIgDraCHz_V396_ski-aRUnfHsFrR0gmB17wxiCFT-uUcsItD/s787/rom.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="551" data-original-width="787" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHNHHpDXREKANSMTD5AE3MKLSICTbRR1MdQ6XKZJObBQlvRbyunXXEVnB1NcHH0YAdK3vC9KyGml5eA_P0T3FN-yX8dedcGu1NjcmVHL7tvwZVD39ymcb0Ih4OWPM4vW4J8ppbL2KtIgDraCHz_V396_ski-aRUnfHsFrR0gmB17wxiCFT-uUcsItD/s320/rom.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-bey6LTqT_levTGDsdBiU0yWeX57WilbJhhMg9djf5vILXHKA8ugYQRqXVjXmkwAZQYC_8c_qgpvjUORna9Cv4fSi6I5NUpr2hbNrDhqbSqIQ48JyAkyNpQ1qQBsRGktj88bU9fiC4IdtO93bIIvedWCQQSpzEK82tvUK4HopGLvRtO9SwJeSF_zc/s787/21.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="551" data-original-width="787" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-bey6LTqT_levTGDsdBiU0yWeX57WilbJhhMg9djf5vILXHKA8ugYQRqXVjXmkwAZQYC_8c_qgpvjUORna9Cv4fSi6I5NUpr2hbNrDhqbSqIQ48JyAkyNpQ1qQBsRGktj88bU9fiC4IdtO93bIIvedWCQQSpzEK82tvUK4HopGLvRtO9SwJeSF_zc/s320/21.gif" width="320" /></a></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghJJYisM9BCkvFwaHwoXgZTv_wfaQ8kS4cLSSHnjWVxEYPUlGoNyadnaRSyoDF_nmB_rjYR5cCa1_CS7b48VlFNCYDM_zpJxuXUW0FRmmbImX3VFNP8m_kvWqOEo0Vx8JL2eFhEH_ixH8xaut9HCgwF4v3jKI9p3Cde1b3uNfHNs-17cLq-MKoobCQ/s787/22.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="551" data-original-width="787" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghJJYisM9BCkvFwaHwoXgZTv_wfaQ8kS4cLSSHnjWVxEYPUlGoNyadnaRSyoDF_nmB_rjYR5cCa1_CS7b48VlFNCYDM_zpJxuXUW0FRmmbImX3VFNP8m_kvWqOEo0Vx8JL2eFhEH_ixH8xaut9HCgwF4v3jKI9p3Cde1b3uNfHNs-17cLq-MKoobCQ/s320/22.gif" width="320" /></a></div><br /><h2 style="text-align: justify;"><span style="background-color: white; color: #050505; font-family: Merriweather, Georgia, serif; font-size: large; text-align: center;">Si lo quieres construir en papel, estos videos te pueden ayudar</span></h2><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="334" src="https://www.youtube.com/embed/P8-uLRDa9Lo" width="490" youtube-src-id="P8-uLRDa9Lo"></iframe></div><p></p><p><br /></p><p><span style="background-color: white; color: #3b170b; font-family: "Times New Roman", serif; font-size: 17.3333px;">Esta publicación</span><span style="background-color: white; color: #3b170b; font-family: "Times New Roman", serif; font-size: 17.3333px; mso-spacerun: yes;"> </span><span style="background-color: white; color: #3b170b; font-family: "Times New Roman", serif; font-size: 17.3333px;">incluye imágenes I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www .peda.com/polypro)</span></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-48835095438223010172022-09-26T09:51:00.000-05:002022-09-26T09:51:05.082-05:00LAS MATEMÁTICAS Y EL ORIGAMI<div class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><span>Jaime Niño Bernal </span><br /></div>
<div class="separator" style="clear: both; text-align: center;">
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-ZO8IqKefxCw/WLJBL1SQceI/AAAAAAAACOs/M-qfbbk96oUgVNzpbUzQwxcnvMM3YCXswCLcB/s1600/60%2B-%2B90-.JPG" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto; text-align: center;"><img border="0" height="240" src="https://2.bp.blogspot.com/-ZO8IqKefxCw/WLJBL1SQceI/AAAAAAAACOs/M-qfbbk96oUgVNzpbUzQwxcnvMM3YCXswCLcB/s320/60%2B-%2B90-.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Modulo 60º - 90º - Diseño Jaime Niño<br />
https://www.flickr.com/photos/jaimeni/7269745594/</td></tr>
</tbody></table>
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</div><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><span style="font-family: "lm roman 10"; font-size: large;"><br /></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><span style="font-family: "lm roman 10"; font-size: large;">El valor del origami se ha venido reconociendo a nivel mundial, este se ha utilizado desde la formación básica para desarrollar la motricidad fina, pasando por la educación secundaria para ayudar a los estudiantes a relacionar formas geométricas con el entorno, y ahora está presente en investigaciones de nivel avanzado como las desarrolladas en la NASA</span><a href="file:///E:/para%20la%20revista%20saberes.docx#_ftn1" name="_ftnref1" style="font-family: "LM Roman 10"; font-size: x-large;" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="line-height: 17.12px;">[1]</span></span></span></a><span style="font-family: "lm roman 10"; font-size: large;">.</span></div>
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<span style="font-family: "lm roman 10";"><span style="font-size: large;">El
pedagogo alemán Federico Frôbel fue el primero en usarlo como herramienta
didáctica en kindergarten. El origami no es sólo aplicable como motivación y
complemento de muchas actividades del aula de educación infantil, primaria y
secundaria, sino como una herramienta para potencializar las diferentes
dimensiones cognitivas del ser humano.</span></span><span style="font-family: "lm roman 10"; font-size: 12pt;"> </span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-J01p_R722gw/WLJIZv87rXI/AAAAAAAACPE/-_rGVRVBD5EcnnyhFU17XCV5HYO5hHKOQCLcB/s1600/IMG_7455.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://3.bp.blogspot.com/-J01p_R722gw/WLJIZv87rXI/AAAAAAAACPE/-_rGVRVBD5EcnnyhFU17XCV5HYO5hHKOQCLcB/s320/IMG_7455.JPG" width="213" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Trabajo en clase de matemáticas<br />
https://www.flickr.com/photos/aulamatematicas/29964839373/</td></tr>
</tbody></table>
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-u7nR8OjOrfE/WLJJIVBr4EI/AAAAAAAACPI/P3Uce_KNJb01FNgjPWh2yK0Q8CjOc8ZqwCLcB/s1600/Gallinas.JPG" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://2.bp.blogspot.com/-u7nR8OjOrfE/WLJJIVBr4EI/AAAAAAAACPI/P3Uce_KNJb01FNgjPWh2yK0Q8CjOc8ZqwCLcB/s320/Gallinas.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Gallinas - Diseño: Jaime Niño<br />
https://www.flickr.com/photos/jaimeni/4728070557/</td></tr>
</tbody></table>
</span><br />
<div>
<!--[if !supportFootnotes]--><span style="font-family: "lm roman 10"; font-size: large;">El catedrático Kawashima Ryuta especializado en la ciencia del cerebro, lleva a cabo su investigación en el Instituto del Desarrollo, Envejecimiento y Cáncer de la Universidad de Tohoku, ha demostrado que hacer </span><i style="font-family: "LM Roman 10"; font-size: x-large;">origami </i><span style="font-family: "lm roman 10"; font-size: large;">aumenta el flujo sanguíneo en la zona prefrontal del cerebro contribuyendo así a su mejor funcionamiento</span><a href="file:///E:/para%20la%20revista%20saberes.docx#_ftn1" name="_ftnref1" style="font-family: "LM Roman 10"; font-size: x-large;" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="line-height: 25.68px;">[2]</span></span></span></a><span style="font-family: "lm roman 10"; font-size: large;">. </span></div>
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<span style="font-family: "lm roman 10"; font-size: large;">El origami es una herramienta muy importante para el estudio de la matemática, específicamente de la geometría. Por ello quien esté preocupado por la didáctica de la matemática no puede dejar de lado este recurso tan motívate para los estudiantes. En clase el plegado de papel se puede utilizar en muchos aspectos del currículo, en general la hoja de papel representa un plano, que en este caso se puede doblar, permitiendo construir cualquier concepto relacionado con la geometría euclidiana.</span></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-ZvBBamkClhc/WLJJ3SZkL_I/AAAAAAAACPQ/kn_ExHejqZ45gQfwQB86P2UBUedLsNiUgCLcB/s1600/IMG_6666.JPG" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" height="266" src="https://1.bp.blogspot.com/-ZvBBamkClhc/WLJJ3SZkL_I/AAAAAAAACPQ/kn_ExHejqZ45gQfwQB86P2UBUedLsNiUgCLcB/s400/IMG_6666.JPG" title="ascdsadxxAx" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Trabajo en clase de matemáticas<br />
https://www.flickr.com/photos/aulamatematicas/26695189716/</td></tr>
</tbody></table>
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<span class="MsoFootnoteReference"><span lang="ES-CO" style="font-family: "lm roman 10";"><span class="MsoFootnoteReference"><a href="file:///E:/para%20la%20revista%20saberes.docx#_ftnref1" name="_ftn1" style="font-family: "Times New Roman";" title=""><span class="MsoFootnoteReference"><span lang="ES-CO" style="font-family: "lm roman 10";"><span class="MsoFootnoteReference"><span lang="ES-CO" style="font-size: 10pt; line-height: 14.2667px;">[1]</span></span></span></span></a><span lang="ES-CO"> Construcción de celdas solares <a href="https://www.nasa.gov/jpl/news/origami-style-solar-power-20140814">https://www.nasa.gov/jpl/news/origami-style-solar-power-20140814</a></span></span></span></span></div>
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</span></i><span lang="ES-CO" style="font-family: "lm roman 10"; mso-bidi-font-family: "Times New Roman";">¡Matemáticas! </span><span lang="ES-CO" style="font-family: "lm roman 10";"><a href="http://web-japan.org/nipponia/nipponia41/es/feature/feature09.html">http://web-japan.org/nipponia/nipponia41/es/feature/feature09.html</a></span><span lang="ES-CO" style="font-family: "times new roman" , "serif";"><o:p></o:p></span></div>
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Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0Caldas, Boyacá, Colombia5.554592 -73.8650890000000125.5506410000000006 -73.870131500000014 5.558543 -73.86004650000001tag:blogger.com,1999:blog-4375388739861338150.post-15586478926098234012022-03-06T22:11:00.003-05:002023-01-16T19:01:20.672-05:00Poliedros: Construcción Rombicuboctaedro<div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="324" src="https://www.youtube.com/embed/BwUBU-Uf_eQ" width="445" youtube-src-id="BwUBU-Uf_eQ"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-d2zQUi8LkIc/VNLEv-uhGQI/AAAAAAAAA-g/TQT9xBVOhro/s1600/rombicuboctaedro.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-d2zQUi8LkIc/VNLEv-uhGQI/AAAAAAAAA-g/TQT9xBVOhro/s1600/rombicuboctaedro.gif" /></a></div>
<br />Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-48382439279688428912022-01-27T20:32:00.000-05:002022-01-27T20:32:22.862-05:00CARTELERA Nº 2<div class="separator" style="clear: both; text-align: center;">
GRADO 8</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-N-WrXedb2_U/T5ImijuiZJI/AAAAAAAAAT4/zkmbAJZVyek/s1600/abril+2+octavo.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="http://2.bp.blogspot.com/-N-WrXedb2_U/T5ImijuiZJI/AAAAAAAAAT4/zkmbAJZVyek/s400/abril+2+octavo.jpg" width="400" /></a></div>
<br />
<div style="text-align: center;">
GRADO 9</div>
<div style="text-align: center;">
<br /></div>
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<a href="http://1.bp.blogspot.com/-jC4B5LxMLG4/T5Imh1xpIgI/AAAAAAAAATw/YhGr8I2rRpY/s1600/abril+2+noveno.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="270" src="http://1.bp.blogspot.com/-jC4B5LxMLG4/T5Imh1xpIgI/AAAAAAAAATw/YhGr8I2rRpY/s400/abril+2+noveno.jpg" width="400" /></a></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
GRADO 10</div>
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<a href="http://1.bp.blogspot.com/-r-Y3nQW0d84/T5Imgo-pCVI/AAAAAAAAATo/qG3AxcTeoY4/s1600/abril+2+d%C3%A9cimo.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="272" src="http://1.bp.blogspot.com/-r-Y3nQW0d84/T5Imgo-pCVI/AAAAAAAAATo/qG3AxcTeoY4/s400/abril+2+d%C3%A9cimo.jpg" width="400" /></a></div>
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GRADO 11</div>
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<a href="http://4.bp.blogspot.com/-2bmLPXiFdzk/T5ImjRxnGSI/AAAAAAAAAUA/OMWEQCnuEaM/s1600/abril+2+once.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="175" src="http://4.bp.blogspot.com/-2bmLPXiFdzk/T5ImjRxnGSI/AAAAAAAAAUA/OMWEQCnuEaM/s400/abril+2+once.jpg" width="400" /></a></div>
<br />Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-54814386451873692762021-12-11T21:57:00.000-05:002021-12-11T21:57:03.479-05:00Reto matemático para grado 8<p style="clear: both; text-align: left;"><span style="font-size: large;">Si tienes alguna duda, pregunta en los comentarios, con gusto te ayudaré</span></p><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-o316v58HVJg/VEgf2FWNOhI/AAAAAAAAA3o/LLdihXdHe4E/s1600/13.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-o316v58HVJg/VEgf2FWNOhI/AAAAAAAAA3o/LLdihXdHe4E/s320/13.png" /></a></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-12323011570137349662021-10-17T14:07:00.001-05:002021-10-17T14:09:07.749-05:00Poliedro: Cubo truncado<p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><h1>Poliedro: Cubo truncado<o:p></o:p></h1>
<p class="MsoNormal" style="text-align: justify;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 12pt; line-height: 107%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">El cubo truncado es uno de los trece poliedros de
Arquímedes (ver <a href="http://origamiymatematicas.blogspot.com/2021/01/jaime-nino-bernal-poliedrosregulares.html" target="_blank">Poliedros Platónicos y Arquimedianos</a>), también conocidos como
poliedro semirregulares o poliedros arquimedianos. Se forma al truncar (cortar)
los vértices de un cubo a un tercio de la longitud de la arista</span><span style="background: white; color: #1a1a1a; font-family: "Times New Roman",serif; font-size: 12pt; line-height: 107%;">.</span> <span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 12pt; line-height: 107%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">se eliminan cuatro pirámides
de base triangular, una en cada vértice</span><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 107%; mso-fareast-language: ES-CO;">
tiene el mismo número de caras que un Cuboctaedro: 14 caras, 8 de ellas son
triángulos equiláteros y 6 de ellas octágonos.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 107%; mso-fareast-language: ES-CO;"> </span></p>
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truncado<o:p></o:p></span></b></p>
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<td style="background: rgb(251, 228, 213); border-top: none; border: 1pt solid rgb(244, 176, 131); mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
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<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 64; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">14</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
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<td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Aristas<o:p></o:p></span></b></p>
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<td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">36<o:p></o:p></span></b></p>
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<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 68; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Vértices</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
<td style="background: rgb(251, 228, 213); border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-background-themecolor: accent2; mso-background-themetint: 51; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 64; text-align: center;"><b><span style="font-family: "Times New Roman", serif; font-size: 12pt;">24</span></b><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span></b></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid rgb(244, 176, 131); mso-border-alt: solid #F4B083 .5pt; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 70.05pt;" valign="top" width="93">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; mso-yfti-cnfc: 4; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Configuración
de vértices<o:p></o:p></span></b></p>
</td>
<td style="border-bottom: 1pt solid rgb(244, 176, 131); border-left: none; border-right: 1pt solid rgb(244, 176, 131); border-top: none; mso-border-alt: solid #F4B083 .5pt; mso-border-bottom-themecolor: accent2; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #F4B083 .5pt; mso-border-left-themecolor: accent2; mso-border-left-themetint: 153; mso-border-right-themecolor: accent2; mso-border-right-themetint: 153; mso-border-themecolor: accent2; mso-border-themetint: 153; mso-border-top-alt: solid #F4B083 .5pt; mso-border-top-themecolor: accent2; mso-border-top-themetint: 153; padding: 0cm 5.4pt; width: 139.95pt;" valign="top" width="187">
<p align="center" class="MsoNormal" style="line-height: 16.8pt; margin-bottom: 8.4pt; margin-left: 0cm; margin-right: 0cm; margin-top: 6.0pt; margin: 6pt 0cm 8.4pt; text-align: center;"><b><span style="font-family: "Times New Roman",serif; font-size: 12pt;">Uniforme de
orden 3<br />
1 <span color="windowtext" style="text-decoration-line: none;">triángulo</span><br />
2 <span color="windowtext" style="text-decoration-line: none;">octágono</span><o:p></o:p></span></b></p>
</td>
</tr>
</tbody></table>
</div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="395" src="https://www.youtube.com/embed/zLKZthIKNZM" width="475" youtube-src-id="zLKZthIKNZM"></iframe></div><br /> <p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-D4F5U86Zls0/YWW46eRWu1I/AAAAAAAAI9I/_7AkOGuHtA4rYf2L3IO9CM1sMIPsNc8bwCLcBGAsYHQ/s560/Cubo%2Btruncado.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="418" data-original-width="560" height="239" src="https://1.bp.blogspot.com/-D4F5U86Zls0/YWW46eRWu1I/AAAAAAAAI9I/_7AkOGuHtA4rYf2L3IO9CM1sMIPsNc8bwCLcBGAsYHQ/s320/Cubo%2Btruncado.gif" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-tDZnzVYTwkk/YWW6YX-jorI/AAAAAAAAI9U/3iA2Zh_ln9oztDwchrACKCdIy4153YulACLcBGAsYHQ/s742/Cubo%2Btruncado...gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="582" data-original-width="742" height="251" src="https://1.bp.blogspot.com/-tDZnzVYTwkk/YWW6YX-jorI/AAAAAAAAI9U/3iA2Zh_ln9oztDwchrACKCdIy4153YulACLcBGAsYHQ/s320/Cubo%2Btruncado...gif" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-lpn7OCZ5tQg/YWW6YUAPR8I/AAAAAAAAI9Q/baF3C79wEeMJaF_4cRdwnFTQKnwi9b8IACLcBGAsYHQ/s742/Cubo%2Btruncado..gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="582" data-original-width="742" height="251" src="https://1.bp.blogspot.com/-lpn7OCZ5tQg/YWW6YUAPR8I/AAAAAAAAI9Q/baF3C79wEeMJaF_4cRdwnFTQKnwi9b8IACLcBGAsYHQ/s320/Cubo%2Btruncado..gif" width="320" /></a></div><br /><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><p class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0cm; vertical-align: baseline;"><span style="color: #3b170b; font-family: "Times New Roman",serif; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">Esta publicación<span style="mso-spacerun: yes;"> </span>incluye imágenes
I modelos realizados con Poly Pro de Pedagoguery Software lnc. (http://www
.peda.com/polypro)<o:p></o:p></span></p><br /></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-78950890901701525162021-10-12T11:55:00.001-05:002022-09-26T09:52:58.810-05:00Poliedros: Pirámides<h2 style="text-align: left;"> <b>Pirámide</b></h2><div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-BFPj2Pg6-Fs/YWW94p9aaaI/AAAAAAAAI9g/ItK4aOdi7q4J56ADbSR2_65K6NX7yGXzwCPcBGAsYHg/s5184/Pir%25C3%25A1mides.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3456" data-original-width="5184" height="264" src="https://1.bp.blogspot.com/-BFPj2Pg6-Fs/YWW94p9aaaI/AAAAAAAAI9g/ItK4aOdi7q4J56ADbSR2_65K6NX7yGXzwCPcBGAsYHg/w397-h264/Pir%25C3%25A1mides.jpg" width="397" /></a></div><br /><b><br /></b></div>
<p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 35.4pt; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span><span style="background: white; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 115%;">La pirámide es
un poliedro</span><span style="background: white; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 115%;"> -sólido geométrico- constituido por un polígono como
base (puede ser cualquier polígono) y triángulos isósceles como caras laterales
(Igual al número de lados del polígono de la base), las caras laterales tienen
un vértice común llamado cúspide o
ápice.</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-pRrhFu7DK0k/YLBVrM1mcvI/AAAAAAAAIRw/mviNBtzoWjcMlcn2aZ6RWz43eNzYiIxawCLcBGAsYHQ/s1882/Pir%25C3%25A1mide.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1559" data-original-width="1882" src="https://1.bp.blogspot.com/-pRrhFu7DK0k/YLBVrM1mcvI/AAAAAAAAIRw/mviNBtzoWjcMlcn2aZ6RWz43eNzYiIxawCLcBGAsYHQ/s320/Pir%25C3%25A1mide.png" width="320" /></a></div><p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 35.4pt; mso-layout-grid-align: none; text-autospace: none;"><br /></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-v5kPHhPKA5c/YLBWo_tsg5I/AAAAAAAAISg/3YU4yUH5oOUjocxShRXo3Go_f-o0G7v3QCLcBGAsYHQ/s1280/pyramids-35150_1280.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="772" data-original-width="1280" src="https://1.bp.blogspot.com/-v5kPHhPKA5c/YLBWo_tsg5I/AAAAAAAAISg/3YU4yUH5oOUjocxShRXo3Go_f-o0G7v3QCLcBGAsYHQ/s320/pyramids-35150_1280.png" width="320" /></a></div><br /><p align="center" class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 35.4pt; mso-layout-grid-align: none; text-align: center; text-autospace: none;"><br /></p>
<p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 35.4pt; mso-layout-grid-align: none; text-autospace: none;"><span style="background: white; color: black; font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%; mso-themecolor: text1;">Características:<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; margin-left: 35.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 35.4pt; mso-layout-grid-align: none; text-autospace: none;"><span style="background: white; color: black; font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p class="MsoListParagraphCxSpFirst" style="line-height: 115%; margin-bottom: 0cm; margin-left: 53.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 53.4pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none; text-indent: -18pt;"><!--[if !supportLists]--><span style="color: black; font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol; mso-themecolor: text1;"><span style="mso-list: Ignore;">·<span style="font: 7pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="background: white; color: black; font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%; mso-themecolor: text1;">El número total de las aristas es doble del número de lados
de la base. <o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="line-height: 115%; margin-bottom: 0cm; margin-left: 53.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 53.4pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none; text-indent: -18pt;"><!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%;">Su número de caras y de vértices se
obtiene sumándole 1 al número de lados del polígono de su base. <o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="line-height: 115%; margin-bottom: 0cm; margin-left: 53.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 53.4pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none; text-indent: -18pt;"><!--[if !supportLists]--><span style="color: black; font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol; mso-themecolor: text1;"><span style="mso-list: Ignore;">·<span style="font: 7pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%;">La base de los triángulos que conforman
sus caras laterales es cada uno de los lados del polígono de su base.<span style="background: white; color: black; mso-themecolor: text1;"><o:p></o:p></span></span></p>
<p class="MsoListParagraphCxSpLast" style="line-height: 115%; margin-bottom: 0cm; margin-left: 53.4pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 53.4pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none; text-indent: -18pt;"><!--[if !supportLists]--><span style="color: black; font-family: Symbol; font-size: 10.5pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol; mso-themecolor: text1;"><span style="mso-list: Ignore;">·<span style="font: 7pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%;">Existen infinitas posibilidades de tipos
de pirámides.</span><span style="background: white; font-family: "Times New Roman", serif; line-height: 115%;"><o:p></o:p></span></p>
<h2 style="line-height: 115%; margin-bottom: 0cm; text-align: left;"><span style="color: red; font-size: small;">Si quieres construir una piramide en origami, te dejo un video de mi canal de Youtube</span></h2><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/DEdl7VaWG0Y" width="320" youtube-src-id="DEdl7VaWG0Y"></iframe></div><span style="color: red; font-size: small;"><br /></span></div><h2 style="text-align: left;">Tipos de pirámides</h2>
<p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%;">Las pirámides se pueden clasificar según
distintos criterios. Además, estos mismos criterios se utilizan para
nombrarlas. <o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman",serif; font-size: 12pt; line-height: 115%;">se clasifican y se nombran según el número
de lados del polígono de la base, según si el polígono de la base es regular o
irregular, si es irregular según si el polígono de la base es convexo o
cóncavo, también, se clasifican según si son rectas, es decir si la cúspide y
el centro de la base están unidas por una línea perpendicular u oblicuas o
inclinadas, otra clasificación corresponde a si están truncadas o no. <o:p></o:p></span></p>
<p style="background: white;"><strong><span style="color: #222222;">1. Pirámide
regular</span></strong><span style="color: #222222;"><o:p></o:p></span></p>
<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-9EeMQ_ZKShc/YLBWUBfJVzI/AAAAAAAAISE/WwpF3QkMzBIpbHHW3MdrMuNw_m5sQec3ACLcBGAsYHQ/s845/Piramide%2Brecta.png" style="clear: left; display: inline; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="845" data-original-width="559" height="320" src="https://1.bp.blogspot.com/-9EeMQ_ZKShc/YLBWUBfJVzI/AAAAAAAAISE/WwpF3QkMzBIpbHHW3MdrMuNw_m5sQec3ACLcBGAsYHQ/s320/Piramide%2Brecta.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="background-color: white; color: #222222; text-align: left;">Se caracteriza por
tener como base un polígono regular y sus caras laterales iguales.</span></div>
<p style="background: white;"><span style="color: #222222;"> </span><strong><span style="color: #222222;">2. Pirámide
irregular</span></strong></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Ul7EILUsgV0/YLBWT_d2auI/AAAAAAAAIR8/1CcBcF9doiE9JFXSpZFupWImHTr8N-EggCLcBGAsYHQ/s788/Piramide%2Birregular.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="788" data-original-width="488" height="320" src="https://1.bp.blogspot.com/-Ul7EILUsgV0/YLBWT_d2auI/AAAAAAAAIR8/1CcBcF9doiE9JFXSpZFupWImHTr8N-EggCLcBGAsYHQ/s320/Piramide%2Birregular.png" /></a></div><p class="MsoNormal" style="background: white;"></p>
<p style="background: white;"><span style="color: #222222;">Se caracteriza por
tener de base un polígono irregular.</span></p><p style="background: white;"><strong><span style="color: #222222;">3. Pirámide
convexa</span></strong></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-3n5DzPNV4zQ/YLBWT6feTyI/AAAAAAAAIR4/-FbzpcFr6B4Nb6BTnczCuBv-oNnE0YGPwCLcBGAsYHQ/s718/Piramide%2Bconvexa.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="718" data-original-width="633" height="320" src="https://1.bp.blogspot.com/-3n5DzPNV4zQ/YLBWT6feTyI/AAAAAAAAIR4/-FbzpcFr6B4Nb6BTnczCuBv-oNnE0YGPwCLcBGAsYHQ/s320/Piramide%2Bconvexa.png" /></a></div><p class="MsoNormal" style="background: white;"></p>
<p style="background: white;"><span style="color: #222222;">Se caracteriza por
tener de base es un polígono convexo.<o:p></o:p></span></p>
<p style="background: white;"><span style="color: #222222;"> </span><strong><span style="color: #222222;">4. Pirámide
cóncava</span></strong></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Yhwwrk20-TU/YLBWT1zOlDI/AAAAAAAAISA/KL-olel2uFcGLvPh-jK_aDmHXxdO1O1CwCLcBGAsYHQ/s859/Piramide%2Bconcava.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="853" data-original-width="859" src="https://1.bp.blogspot.com/-Yhwwrk20-TU/YLBWT1zOlDI/AAAAAAAAISA/KL-olel2uFcGLvPh-jK_aDmHXxdO1O1CwCLcBGAsYHQ/s320/Piramide%2Bconcava.png" width="320" /></a></div><p class="MsoNormal" style="background: white;"></p>
<p style="background: white;"><span style="color: #222222;">Se caracteriza por
tener de base es un polígono cóncavo.<o:p></o:p></span></p>
<p style="background: white;"><span style="color: #222222;"> </span><strong><span style="color: #222222;">5. Pirámide
recta</span></strong></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/--qLrHO6KJt0/YLBWUsuDF6I/AAAAAAAAISI/fHcUAJhycvEAgOxPdNPtsU5Bgxhkxe-VQCLcBGAsYHQ/s592/Piramide%2Bregular.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="592" data-original-width="413" height="320" src="https://1.bp.blogspot.com/--qLrHO6KJt0/YLBWUsuDF6I/AAAAAAAAISI/fHcUAJhycvEAgOxPdNPtsU5Bgxhkxe-VQCLcBGAsYHQ/s320/Piramide%2Bregular.png" /></a></div><p class="MsoNormal" style="background: white;"></p>
<p style="background: white;"><span style="color: #222222;">Es aquella en la que
todas sus caras laterales son triángulos isósceles y la altura cae al punto
medio de la base.<o:p></o:p></span></p>
<p style="background: white;"><span style="color: #222222;"> </span><strong><span style="color: #222222;">6. Pirámide
oblícua</span></strong></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-CbPMIkGakv4/YLBWUndbwdI/AAAAAAAAISM/0Slr99p6X2AelxC3ni5GxZhXn853YpPtgCLcBGAsYHQ/s1011/Pir%25C3%25A1mide%2Boblicua.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1011" data-original-width="604" height="320" src="https://1.bp.blogspot.com/-CbPMIkGakv4/YLBWUndbwdI/AAAAAAAAISM/0Slr99p6X2AelxC3ni5GxZhXn853YpPtgCLcBGAsYHQ/s320/Pir%25C3%25A1mide%2Boblicua.png" /></a></div><p class="MsoNormal" style="background: white;"></p>
<p style="background: white;"><span style="color: #222222;">Es aquella en la que
alguna de sus caras laterales no es un triángulo isósceles.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 115%; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;"><span style="background: white; color: black; font-family: "Times New Roman",serif; font-size: 10.5pt; line-height: 115%; mso-themecolor: text1;"><o:p> </o:p></span></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-19277597274173188592021-02-02T08:06:00.003-05:002021-02-11T19:00:48.847-05:00EJERCICIOS DE RAZONAMIENTO MATEMÁTICO - ACEPTA EL RETO<p><span style="font-size: large;"> Si quieres aceptar el reto, puedes dejar tus respuestas en los comentarios, si tienes alguna duda, déjala ahí también, con gusto te ayudare.</span></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-4jYJjXSZoyY/YBlNCLazX_I/AAAAAAAAHmw/ajT6m9-X-aohe3_AqTsOfOs4Orc2uRB2ACLcBGAsYHQ/s1000/37.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="548" data-original-width="1000" height="219" src="https://1.bp.blogspot.com/-4jYJjXSZoyY/YBlNCLazX_I/AAAAAAAAHmw/ajT6m9-X-aohe3_AqTsOfOs4Orc2uRB2ACLcBGAsYHQ/w400-h219/37.jpg" width="400" /></a></div><div><br /></div><div><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Brv4EjEAA3A/YBlNCIEMGmI/AAAAAAAAHms/qhh9Ki9-taUTu-lTawABpuxVvOFxGveeACLcBGAsYHQ/s992/64.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="956" data-original-width="992" height="385" src="https://1.bp.blogspot.com/-Brv4EjEAA3A/YBlNCIEMGmI/AAAAAAAAHms/qhh9Ki9-taUTu-lTawABpuxVvOFxGveeACLcBGAsYHQ/w400-h385/64.jpg" width="400" /></a></div><div><br /></div><div><br /></div><div><br /></div><div style="text-align: center;"><span style="font-size: large;">Encuentra el valor de cada letra</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-6JXyhHU20-Y/YBlNB1TziNI/AAAAAAAAHmo/rWuVTcpl76ojPt6qL-AZpVRaIY3_Y1RMQCLcBGAsYHQ/s642/74.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="315" data-original-width="642" height="196" src="https://1.bp.blogspot.com/-6JXyhHU20-Y/YBlNB1TziNI/AAAAAAAAHmo/rWuVTcpl76ojPt6qL-AZpVRaIY3_Y1RMQCLcBGAsYHQ/w400-h196/74.jpg" width="400" /></a></div><br /><p><br /></p>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-26605818540056394312019-04-05T11:33:00.001-05:002021-02-11T19:02:26.540-05:00Estelación del Dodecaedro<span style="font-size: large;">Dejo el diagrama para la construcción de una de las estelaciones del dodecaedro, para su construcción se necesitan 30 hojas cuadradas.</span><div><span style="font-size: medium;"><br /></span>
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<a href="https://3.bp.blogspot.com/-Qi2jyYNJ2ME/XKeDDhxwYgI/AAAAAAAAFhA/pVEqJTO0-nUiIqhft7UAT5ex7ytU_dOywCLcBGAs/s1600/Estelaci%25C3%25B3n%2Bdel%2Bdodecaedro.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1180" height="640" src="https://3.bp.blogspot.com/-Qi2jyYNJ2ME/XKeDDhxwYgI/AAAAAAAAFhA/pVEqJTO0-nUiIqhft7UAT5ex7ytU_dOywCLcBGAs/s640/Estelaci%25C3%25B3n%2Bdel%2Bdodecaedro.jpg" width="472" /></a></div>
<br /></div>Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0tag:blogger.com,1999:blog-4375388739861338150.post-75747729876284656482017-04-21T08:34:00.000-05:002017-04-21T08:34:11.423-05:00RETO 7<div class="separator" style="clear: both; text-align: center;">
<a href="https://4.bp.blogspot.com/-o_Us4-mywEM/WPoJanjT40I/AAAAAAAACS8/ee9Z60TaEMkLA625Cm_pyYHUdjgmMeqhwCLcB/s1600/130.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="155" src="https://4.bp.blogspot.com/-o_Us4-mywEM/WPoJanjT40I/AAAAAAAACS8/ee9Z60TaEMkLA625Cm_pyYHUdjgmMeqhwCLcB/s400/130.png" width="400" /></a></div>
<br />Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0Caldas, Boyacá, Colombia5.554592 -73.8650890000000125.5506410000000006 -73.870131500000014 5.558543 -73.86004650000001tag:blogger.com,1999:blog-4375388739861338150.post-51744964658884187712017-04-15T22:30:00.000-05:002017-04-19T15:06:44.150-05:00RETO 6<div class="separator" style="clear: both; text-align: center;">
<a href="https://2.bp.blogspot.com/-NA-MMcF6jY4/WPLkbUInvJI/AAAAAAAACSk/7BZ2HOAjifYUoBh6AiwkeiRTQqu1a4KgQCLcB/s1600/42.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="273" src="https://2.bp.blogspot.com/-NA-MMcF6jY4/WPLkbUInvJI/AAAAAAAACSk/7BZ2HOAjifYUoBh6AiwkeiRTQqu1a4KgQCLcB/s320/42.png" width="320" /></a></div>
<br />Jaime Niño Bernal @Jaimeninobhttp://www.blogger.com/profile/06844175947852662080noreply@blogger.com0Caldas, Boyacá, Colombia5.554592 -73.8650890000000125.5506410000000006 -73.870131500000014 5.558543 -73.86004650000001