tag:blogger.com,1999:blog-79275420245677241472024-03-13T06:34:39.295-07:00Geometria del EspacioRomina Cazóhttp://www.blogger.com/profile/14094600100043974596noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-7927542024567724147.post-84825986909574223442012-09-11T05:41:00.000-07:002012-09-18T06:09:36.930-07:00Poliedro<!--[if gte mso 9]><xml>
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<b><span style="font-size: large;"><span style="font-family: "Verdana","sans-serif";">Poliedros</span></span></b></div>
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<b><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;"> </span></b><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Son aquellos
cuerpos geométricos cerrados, limitados por polígonos. Las caras del poliedro
forman la superficie del poliedro </span><span style="font-family: "Verdana","sans-serif";">y
encierran un volumen finito</span><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">.</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 11.0pt; line-height: 115%;">Los poliedros se conciben
como cuerpos tridimensionales, pero hay semejantes topológicos del concepto en
cualquier dimensión. Así, el punto o vértice es el semejante topológico del
poliedro en cero dimensiones, una arista o segmento lo es en 1 dimensión, el
polígono para 2 dimensiones; y el<span style="mso-spacerun: yes;">
</span>polícoro el de cuatro dimensiones. Todas estas formas son conocidas como
politopos, por lo que podemos definir un poliedro como un <b>polítopo
tridimensional</b>.</span></div>
<div style="line-height: 115%; margin-top: 0cm;">
<span style="font-family: "Verdana","sans-serif"; font-size: 11.0pt; line-height: 115%;">Los poliedros son
denominados de acuerdo a su número de caras. Su designación se basa en el
griego clásico. Por ejemplo tetraedro (4-caras), pentaedro (5), hexaedro (6),
heptaedro (7), icosaedro (20) - icosa es 20 en griego clásico -, etc.</span></div>
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<b><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: Arial; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">POLIEDROS REGULARES</span></b></div>
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concurre el mismo número de caras y aristas.</span></div>
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llamado <i>Tecteco </i>fue el primero en formular una teoría general, dando la
construcción geométrica de los cinco cuerpos geométricos poliedros regulares, y
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<span style="font-family: "Verdana","sans-serif";">Un <b>tetraedro</b>
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<a href="http://3.bp.blogspot.com/-BnkKCoaMHig/UE8uJSLhbzI/AAAAAAAAABI/nuJ1CI3cJwM/s1600/Hexaedro+o+cubo.2.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-BnkKCoaMHig/UE8uJSLhbzI/AAAAAAAAABI/nuJ1CI3cJwM/s200/Hexaedro+o+cubo.2.jpg" width="194" /></a><span style="font-family: "Verdana","sans-serif"; font-size: 11.0pt; line-height: 115%;">Un <b>cubo</b> o <b>hexaedro regular</b> es
un poliedro de seis caras cuadradas congruentes, siendo uno de los llamados
sólidos platónicos.Un cubo, además de ser un hexaedro, puede ser clasificado
también como paralelepípedo, recto y rectángulo, pues todas sus caras son de
cuatro lados y paralelas dos a dos, e incluso como un prisma de base
cuadrangular y altura equivalente al lado de la base.</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 11.0pt; line-height: 115%;">Un <b>octaedro</b> es un poliedro de ocho
caras. Con este número de caras puede ser un poliedro convexo o un poliedro
cóncavo. Sus caras han de ser polígonos de siete lados o menos. Si las ocho
caras del octaedro son triángulos equiláteros, iguales entre sí, el octaedro es
convexo y se denomina <b>regular</b>, siendo una figura de los llamados sólidos
platónicos</span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Dodecaedro</span></b></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 11.0pt; line-height: 115%;">Es un poliedro de doce caras, convexo o
cóncavo. Sus caras han de ser polígonos de once lados o menos. Si las doce
caras del dodecaedro son pentágonos regulares, iguales entre sí, el dodecaedro
es convexo y se denomina <i>regular</i>, siendo entonces uno de los llamados
sólidos platónicos.</span></div>
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<a href="http://2.bp.blogspot.com/-Y9kvx__EGqA/UE8wLsxCXXI/AAAAAAAAABg/6DywkjvJv7k/s1600/Icosaedro.5.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="184" src="http://2.bp.blogspot.com/-Y9kvx__EGqA/UE8wLsxCXXI/AAAAAAAAABg/6DywkjvJv7k/s200/Icosaedro.5.jpg" width="200" /></a><span style="font-family: "Verdana","sans-serif";">Un <b>icosaedro</b>
es un poliedro de veinte caras, convexo o cóncavo. Si las veinte caras del
icosaedro son triángulos equiláteros, iguales entre sí, el icosaedro es convexo
y se denomina <i>regular</i>, siendo entonces uno de los llamados sólidos
platónicos. El poliedro conjugado del icosaedro es el dodecaedro.</span></div>
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<b><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">POLIEDROS IREGULARES</span></b></div>
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<span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Son los poliedros cuyas caras son irregulares o desiguales entre estos
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aquellos poliedros que tienen dos bases de la misma forma y sus caras laterales
son rectangulares; así pues no todas sus caras son iguales.</span><br />
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<br />
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm; mso-margin-top-alt: auto;">
<a href="http://4.bp.blogspot.com/-Oe6BH75QX0A/UE817MEqqoI/AAAAAAAAABw/Ic9ffsRj1Wc/s1600/prisma-rectangular.6.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Oe6BH75QX0A/UE817MEqqoI/AAAAAAAAABw/Ic9ffsRj1Wc/s1600/prisma-rectangular.6.png" /></a><b style="color: magenta;"><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Prisma Rectangular</span></b></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";">En el caso
en que las caras laterales sean rectangulares, se llama <span style="mso-bidi-font-weight: bold;">prisma<b> </b>rectangular</span>. El <i>prisma rectangular</i> o </span><a href="http://es.wikipedia.org/wiki/Cuboide" title="Cuboide"><i><span style="color: windowtext; font-family: "Verdana","sans-serif"; text-decoration: none; text-underline: none;">cuboides</span></i></a><span style="font-family: "Verdana","sans-serif";">,
y el <i>prisma octagonal</i> se encuentran entre los tipos de prisma recto, con
una base rectangular y octagonal, respectivamente.</span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Prisma triangular </span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";"><br /></span>
<span style="font-family: "Verdana","sans-serif";"><br /></span>
<span style="font-family: "Verdana","sans-serif";"><br /></span>
<a href="http://2.bp.blogspot.com/-mX6cn1I33ws/UE82HIFPfJI/AAAAAAAAAB4/lhqEmrDIVHA/s1600/prisma+triangular.7.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-mX6cn1I33ws/UE82HIFPfJI/AAAAAAAAAB4/lhqEmrDIVHA/s200/prisma+triangular.7.png" width="93" /></a><span style="font-family: "Verdana","sans-serif";"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";"><br /></span></div>
<div class="MsoNormal" style="color: magenta;">
<span style="font-family: "Verdana","sans-serif";"><b>Un prisma
triangular</b> </span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";"> Es un poliedro formado por dos bases triangulares iguales y
paralelas, y 3 caras que unen los lados correspondientes.</span><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<a href="http://2.bp.blogspot.com/-my1m2YsU4YA/UFhfb1W4neI/AAAAAAAAACc/8JzZJg-Jgno/s1600/Prismas+cuadrangulares.8.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-my1m2YsU4YA/UFhfb1W4neI/AAAAAAAAACc/8JzZJg-Jgno/s200/Prismas+cuadrangulares.8.png" width="120" /></a><span style="font-family: "Verdana","sans-serif";"> </span></div>
<div class="MsoNormal" style="color: magenta;">
<br /></div>
<div class="MsoNormal" style="color: magenta;">
<b><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Prismas cuadrangulares</span></b></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";">Un prisma
cuadrangular es un poliedro que consta de dos caras iguales y paralelas
llamadas bases, y de caras laterales que son paralelogramos.</span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm; mso-margin-top-alt: auto;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm; mso-margin-top-alt: auto;">
<br />
<br />
<br />
<br /></div>
<div class="MsoNormal" style="color: magenta; margin-bottom: 0cm; text-align: center;">
<b><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Las pirámides</span></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm; mso-margin-top-alt: auto;">
<span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Son los poliedros que tienen una base, sus caras laterales son
triángulos y los vértices de los triángulos se unen en un punto llamado
Cúspide, el cual es opuesto a la base.</span><br />
<br />
<a href="http://4.bp.blogspot.com/-m7eQFvP9S9g/UFhfsxI5iDI/AAAAAAAAACk/v67bd6oqXmc/s1600/Pir%C3%A1mide+triangular.9.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-m7eQFvP9S9g/UFhfsxI5iDI/AAAAAAAAACk/v67bd6oqXmc/s200/Pir%C3%A1mide+triangular.9.png" width="168" /></a><span style="font-family: "Verdana","sans-serif";"> </span></div>
<div class="MsoNormal" style="color: magenta;">
<br /></div>
<div class="MsoNormal" style="color: magenta;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Pirámide
triangular</span></b></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";">Figura
sólida que tiene cuatro caras planas triangulares. Si las cuatro caras son
triángulos equiláteros congruentes, se le llama tetraedro. </span></div>
<div class="MsoNormal">
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<a href="http://1.bp.blogspot.com/-LPpURaqoz1k/UFhgg7lIHCI/AAAAAAAAACs/JmcyCAGygss/s1600/Pir%C3%A1mide+cuadrangular.10.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="198" src="http://1.bp.blogspot.com/-LPpURaqoz1k/UFhgg7lIHCI/AAAAAAAAACs/JmcyCAGygss/s200/Pir%C3%A1mide+cuadrangular.10.png" width="200" /></a></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;"> <span style="color: magenta;"> </span><b style="color: magenta;">Pirámide cuadrangular</b></span></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";">Pirámide
que tiene base cuadrangular y cuatro caras triangulares congruentes.</span><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<a href="http://1.bp.blogspot.com/-OfXMMwUIn6w/UFhhTjwslzI/AAAAAAAAAC8/dCjS9plJNN0/s1600/Pir%C3%A1mide+pentagonal.11.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-OfXMMwUIn6w/UFhhTjwslzI/AAAAAAAAAC8/dCjS9plJNN0/s200/Pir%C3%A1mide+pentagonal.11.jpg" width="184" /></a><span style="font-family: "Verdana","sans-serif";"> </span><br />
<br /></div>
<div class="MsoNormal" style="color: magenta;">
<br /></div>
<div class="MsoNormal" style="color: magenta;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Verdana","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CR;">Pirámide
pentagonal</span></b></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif";">Es una
pirámide de base pentagonal sobre la cual se erigen cinco caras triangulares
que se encuentran en un punto, la cúspide. Al igual que cualquier pirámide,
es<span style="mso-spacerun: yes;"> </span>autodual.</span><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br /></div>
<div class="MsoNormal" style="text-align: center;">
<span style="color: magenta;"> </span><b style="color: magenta; font-family: Verdana,sans-serif;">Clasificación de los poliedros</b></div>
<div style="line-height: 115%;">
<span style="font-family: "Verdana","sans-serif"; font-size: 11.0pt; line-height: 115%;">Los poliedros pueden ser clasificados en
muchos grupos según la familia de donde provienen o de las características que
los diferencian; según sus características, se distinguen:</span></div>
<ul type="disc">
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Verdana","sans-serif";">Convexos, como el cubo, o el tetraedro, cuando
cualquier par de puntos del espacio que estén dentro del cuerpo los une un
segmento de recta también interno. En el caso de que dicho segmento se
salga del cuerpo se dice que son poliedros cóncavos, como es el caso del
toroide facetado y los sólidos de karim.</span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Verdana","sans-serif";">Poliedro de caras regulares, cuando todas las
caras del poliedro son polígonos regulares.</span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Verdana","sans-serif";">Poliedro de caras uniformes, cuando todas las
caras son iguales.</span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Verdana","sans-serif";">Se dice poliedro de aristas uniformes cuando los
pares de caras que se reúnen en cada arista son iguales.</span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Verdana","sans-serif";">Se dice poliedro de vértices uniformes cuando en todos
los vértices del poliedro convergen el mismo número de caras y en el mismo
orden.</span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Verdana","sans-serif";">Se dice poliedro regular o regular y uniforme,
como el tetraedro o el icosaedro, cuando es de caras regulares, de caras
uniformes de vértices uniformes y de aristas uniformes.</span></li>
</ul>
<div style="color: magenta;">
<b><br /></b></div>
<div style="color: magenta; font-family: Verdana,sans-serif;">
<b>Definición de poliedro.</b></div>
<br />
<br />
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