Simple polytope

Not to be confused with Simplicial polytope.
Three-dimensional associahedron. Each vertex has three neighboring edges and faces, so this is a simple polyhedron.

In geometry, a d-dimensional simple polytope is a d-dimensional polytope each of whose vertices are adjacent to exactly d edges (also d facets). The vertex figure of a simple d-polytope is a (d – 1)-simplex.[1]

Simple polytopes are topologically dual to simplicial polytopes. The family of polytopes which are both simple and simplicial are simplices or two-dimensional polygons. A simple polyhedron is a three-dimensional polyhedron whose vertices are adjacent to three edges and three faces. The dual to a simple polyhedron is a simplicial polyhedron, in which all faces are triangles.[2]

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