The five regular solids, also called the Platonic solids, are well known. If you have these as models to work with now, you will find that the notion of duality can very easily be illustrated with regard to them.

The tetrahedron is the simplest of all polyhedra. It has only four faces, each of which is an equilateral triangle. It has four trigonal vertices, which means that three face angles surround each vertex. Finally, it has six edges. You see immediately that an interchange in number and kind of faces and vertices leaves the number four unchanged. Because the dual of any polyhedron always keeps the same number of edges as the original from which it is derived, the number six must be kept for the number of edges. This simple description shows you that the tetrahedron is its own dual; that is, the dual of a tetrahedron is another tetrahedron.

If you look now at the octahedron, you see that it has eight faces, each of which is an equilateral triangle. It has six vertices, which can be called tetragonal, because four face angles surround each vertex. Finally, it has twelve edges. An interchange in number and kind of faces and vertices implies that its dual must have eight trigonal vertices and six tetragonal faces, and its edges must still number twelve.