as geometric polyhedra. Starting with any given polyhedron, the dual of its dual is the original polyhedron.

Duality preserves the symmetries of a polyhedron. Therefore, for many classes of polyhedra defined by their symmetries, the duals belong to a corresponding symmetry class. For example, the regular polyhedrathe (convex) Platonic solids and (star) Kepler-Poinsot polyhedraform dual pairs, where the regular tetrahedron