Simplicial polytope

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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.


Simplicial polyhedra include:

Simplicial tilings:

Simplicial 4-polytopes include:

Simplicial higher polytope families:

See also[edit]


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