Polyhedron
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Polyhedron  

About  
Rank  3  
Plural  Polyhedra  
Facet name  Face  
Counts  
Regular convex polyhedra  5  
Regular star polyhedra  4  
Regular finite compounds  1  
Regular tesselations  3  
Regular finite skew polyhedra of full rank  9  
Regular skew apeirotopes  27  
Hierarchy  

A polyhedron or 3polytope is a polytope of rank 3. The facets of polyhedra are polygons, which are called its faces.
Definition[edit  edit source]
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[edit  edit source]
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.
External links[edit  edit source]
 Wikipedia contributors. "Polyhedron".
 Weisstein, Eric W. "Polyhedron" at MathWorld.
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