Dual polyhedron

In geometry, every polyhedron is related to a dual polyhedron. The vertices (points) of one polyhedron match with the faces (flat surfaces) of the other. The edges connecting vertices in one polyhedron match with the edges connecting faces of the other. Starting with any given polyhedron, the dual of its dual is the original polyhedron. 
Of the five platonic polyhedra, only the tetrahedron is dual to itself. The cube and octahedron are dual, and the dodecahedron and icosahedron are dual.