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Simplicial polytope
Polytope whose facets are all simplices / From Wikipedia, the free encyclopedia
Not to be confused with Simple polytope.
In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions contains only triangular faces[1] and corresponds via Steinitz's theorem to a maximal planar graph.
![Multicolored representation of a pentagonal bipyramid](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Pentagonale_bipiramide.png/640px-Pentagonale_bipiramide.png)
They are topologically dual to simple polytopes. Polytopes which are both simple and simplicial are either simplices or two-dimensional polygons.