# Difference between revisions of "Polyhedron"

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− | 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. | + | 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. |

== Classification == | == Classification == | ||

===Concavity=== | ===Concavity=== | ||

− | Polyhedra can be [[convex]] or [[concave]]. | + | Polyhedra can be [[convex polyhedron | convex]] or [[concave polyhedron | concave]]. |

===Number of sides=== | ===Number of sides=== | ||

Line 17: | Line 17: | ||

== Surface area == | == Surface area == | ||

− | The [[surface area]] of a polyhedron is the sum of its sides. | + | The [[surface area]] of a polyhedron is the sum of the areas of its sides. |

== Volume == | == Volume == | ||

+ | 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. | ||

== Angles == | == Angles == | ||

== Related figures == | == Related figures == | ||

− | * | + | * Polyhedral solids are the union of a polyhedron and the space that it encloses. |

* [[Polygon]]s | * [[Polygon]]s | ||

− | * | + | * Polytopes |

{{stub}} | {{stub}} | ||

[[Category:geometry]] | [[Category:geometry]] |

## Latest revision as of 22:15, 6 December 2016

A polyhedron is a three-dimensional surface composed of at least four flat faces which encloses a region of space. These faces intersect in edges and vertices. Polyhedra are 3-D analogues of polygons. They can be thought of as sets of ordered triples.

## Contents

## Classification

### Concavity

Polyhedra can be convex or concave.

### Number of sides

### Regular polyhedra

They have congruent faces, angles, and edges. Only regular tetrahedra, hexahedra (cubes), octahedra, dodecahedra, and icosahedra exist. (In addition, a sphere could be thought of a polyhedron with an infinite number of faces.)

## Common polyhedra

The polyhedra most commonly encountered include:

- tetrahedron - 4 faces
- hexahedron - 6 faces

etc.

Prisms and pyramids can be polyhedra.

## Surface area

The surface area of a polyhedron is the sum of the areas of its sides.

## Volume

The volume of a certain polyhedron is defined as , where B is the area of the base of the polyhedron and h is the height to this base.

## Angles

## Related figures

- Polyhedral solids are the union of a polyhedron and the space that it encloses.
- Polygons
- Polytopes

*This article is a stub. Help us out by expanding it.*