https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=XK-39&feedformat=atom AoPS Wiki - User contributions [en] 2022-01-27T21:43:15Z User contributions MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=Polyhedron&diff=32122 Polyhedron 2009-06-11T18:53:05Z <p>XK-39: /* Volume */</p> <hr /> <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 /> <br /> == Classification ==<br /> ===Concavity===<br /> Polyhedra can be [[convex polyhedron | convex]] or [[concave polyhedron | concave]].<br /> <br /> ===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 /> <br /> [[Prism]]s and [[pyramid]]s can be polyhedra.<br /> <br /> == Surface area ==<br /> The [[surface area]] of a polyhedron is the sum of the areas of its sides.<br /> <br /> == Volume ==<br /> The [[volume]] of a certain polyhedron is defined as &lt;math&gt;(B)h&lt;/math&gt;, where B is the area of the base of the polyhedron and h is the height to this base.<br /> <br /> == Angles ==<br /> <br /> == 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 /> {{stub}}<br /> [[Category:geometry]]</div> XK-39