Simplicial polytope

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

Simplicial polyhedra include:

Simplicial tilings:

Simplicial 4-polytopes include:

Simplicial higher polytope families:

See also

Notes

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

References


This article is issued from Wikipedia - version of the Thursday, September 25, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.