# Polyhedron

Polyhedron
Rank3
PluralPolyhedra
Facet nameFace
Counts
Regular convex polyhedra5
Regular star polyhedra4
Regular finite compounds1
Regular tesselations3
Regular finite skew polyhedra of full rank9
Regular skew apeirotopes27
Hierarchy
 ← Polygon Polyhedron Polychoron → 2 3 4

A polyhedron or 3-polytope is a polytope of rank 3. The facets of polyhedra are polygons, which are called its faces.

## Definition

Polyhedra can be defined to be polytopes of rank 3. Since the meaning of polytope differs depending on context the meaning of polyhedra also differs.

The term polyhedron may occasionally be used as a synonym for polytope. For example associahedra, despite its suffix, are not necessarily rank 3.

## Regular polyhedra

A regular polyhedron is a polyhedron whose flags are identical under its symmetry group. All regular polyhedra are uniform, isogonal, isotoxal, isohedral, and noble. In 3D Euclidean space, there are 9 finite regular polyhedra and 3 tilings that are not skew, 9 finite skew polyhedra, and 27 regular skew apeirohedra.