# Difference between revisions of "Polyhedron"

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.

## Classification

### Concavity

Polyhedra can be convex or concave.

### 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:

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 $(B)h$, where B is the area of the base of the polyhedron and h is the height to this base.

## Related figures

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