High Quality Content by WIKIPEDIA articles! In geometry, a d-dimensional simple polytope is a d-dimensional polytope each of whose vertices is adjacent to exactly d edges (also d facets). The vertex figure of a simple d-polytope is a (d-1)-simplex. They are topologically dual to simplicial polytopes. The family of polytopes which are both simple and simplicial are simplices or two-dimensional polygons. For example, a simple polyhedron is a polyhedron whose vertices are adjacent to 3 edges and 3 faces. And the dual to a simple polyhedron is a simplicial polyhedron, containing all triangular faces.

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