Polyhedron
From AoPSWiki
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.
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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
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