https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=XK-39&feedformat=atomAoPS Wiki - User contributions [en]2022-01-27T21:43:15ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Polyhedron&diff=32122Polyhedron2009-06-11T18:53:05Z<p>XK-39: /* Volume */</p>
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<div>A polyhedron is a three-dimensional surface composed of at least four flat [[face]]s which encloses a region of [[space]]. These faces intersect in [[edge]]s and [[vertex|vertices]]. Polyhedra are 3-D analogues of [[polygon]]s. They can be thought of as sets of [[ordered]] triples.<br />
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== Classification ==<br />
===Concavity===<br />
Polyhedra can be [[convex polyhedron | convex]] or [[concave polyhedron | concave]].<br />
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===Number of sides===<br />
===Regular polyhedra===<br />
They have congruent faces, angles, and edges. Only regular tetrahedra, hexahedra ([[cube]]s), octahedra, dodecahedra, and icosahedra exist. (In addition, a [[sphere]] could be thought of a polyhedron with an infinite number of faces.)<br />
== Common polyhedra ==<br />
The polyhedra most commonly encountered include:<br />
* [[tetrahedron]] - 4 faces<br />
* [[hexahedron]] - 6 faces<br />
etc.<br />
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[[Prism]]s and [[pyramid]]s can be polyhedra.<br />
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== Surface area ==<br />
The [[surface area]] of a polyhedron is the sum of the areas of its sides.<br />
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== Volume ==<br />
The [[volume]] of a certain polyhedron is defined as <math>(B)h</math>, where B is the area of the base of the polyhedron and h is the height to this base.<br />
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== Angles ==<br />
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== Related figures ==<br />
* [[Polyhedral solid]]s are the union of a polyhedron and the space that it encloses.<br />
* [[Polygon]]s<br />
* [[Polytope]]s<br />
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[[Category:geometry]]</div>XK-39