Simplicial polytope

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In geometry, a simplicial polytope is a polytope whose facets are all simplices.

For example, a simplicial polyhedron in 3 dimensions contains only triangular faces[1] and corresponds via Steinitz's theorem to a maximal planar graph.

They are topologically dual to simple polytopes. Polytopes which are both simple and simplicial are either simplices or two-dimensional polygons.

Examples[edit]

Simplicial polyhedra include:

Simplicial tilings:

Simplicial 4-polytopes include:

Simplicial higher polytope families:

Notes[edit]

  1. ^ Polyhedra, Peter R. Cromwell, 1997. (p.341)

References[edit]

See also[edit]