dual polyhedron

In geometry, polyhedra are associated into pairs called duals, where the of one correspond to the faces of the other. Starting with any given polyhedron, the dual of its dual is the original polyhedron. The dual of an isogonal polyhedron, having equivalent vertices, is one which is isohedral, having equivalent faces, and of one which is isotoxal, having equivalent edges, is also isotoxal. The regular polyhedra — the Platonic solids and Kepler-Poinsot polyhedra — form dual pairs, with the exception of the regular tetrahedron which is self-dual.