# Polyhedron

solid in three dimensions with flat faces
(Redirected from Polyhedra)

A polyhedron (polyhedra or polyhedrons if more than one) is a geometrical shape. It is a 3D shape with flat faces, and straight edges. Each face is a polygon surrounded by edges. Usually it is known by the number of faces, corners, or edges it has.

There are many groups of polyhedra, which can either be only a small set, or can be infinite. Prisms, pyramids, antiprisms, and bipyramids are groups of polyhedra.

A regular polyhedron has faces that are all the same, corners that are all the same, and edges that are all the same. A uniform polyhedron can have one or two kinds of its parts be all the same.

## Definition

Two types of polyhedron are convex and concave. The edge connecting any two points of a convex polyhedron is inside the polyhedron. The line connecting two points of a concave polyhedron may go outside the polyhedron. The Platonic solids are regular convex polyhedra.

Mathematicians do not always agree on what makes a polyhedron. Some may only consider the convex polyhedra, and disregard the ones that are not convex. Some polyhedra are degenerate, meaning that when drawn as real objects, they look flat.

### Naming

Usually, polyhedra are named by the number of faces they have. The first polyhedra are the tetrahedron, which is made of four triangles, pentahedron (five faces, can look like a four-sided pyramid), hexahedron (six faces, a cube if it is regular), heptahedron (seven faces) and octahedron (eight faces). Prisms, pyramids and other shapes can also be named after how many faces they have.