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What is simple/simplicial polytope?

A -polytope is called **simple** if each vertex is contained
in exactly facets. A -polytope is called **simplicial**
if each facet contains exactly vertices. By definition,
a dual of simple (simlicial)
polytope is simplicial (simple, respectively).
Every facet of a simplicial -polytope is a -simplex. Each vertex
of a simple -polytope is contained in exactly -edges.

A -cube is a simple polytope and a -simplex is both simple and
simplicial.

Komei Fukuda
2004-08-26