Dual polytope

A dual polytope is a polytope related to the base polytope through the correlation of its vertices with the other's facets and vice versa. The number of elements of a dual polytope follow a reverse pattern to the base polytope, and share the same symmetry. The cells of a dual polytope are given by the duals of the vertex figure(s) of the base polytope.

If the dual polytope is topologically equivalent to the base polytope, then it is called a self-dual polytope.

Among the regular polytopes, the regular polygons and the simplex are self-dual, while the hypercube and the cross polytope form dual pairs. The three- and four-dimensional pentagonal polytopes also come in dual pairs.