Plato’s Solids and Cayley’s Theorem

There are five convex regular solids, the tetrahedron (four triangular faces), cube (six square faces), octahedron (eight triangular faces), dodecahedron (twelve pentagonal faces), and icosahedron (twenty triangular faces). They are illustrated in Figure 8.1. We have already shown that the group of rotational symmetries of the tetrahedron is isomorphic to the alternating group A4. In this chapter we shall produce analogous results for the other four solids.