The table below lists the number of edges, vertices, and faces of the five Platonic solids. The table shows that for each Platonic solid we have the relation Name of polyhedron Number V of vertices quotation Number E of edges Number F of faces tetrahedron 4 6 4 cube 8 12 6 octahedron 6 12 8 dodecahedron 20 30 12 icosahedron 12 30 20 $$V - E + F = 2$$ (6) It is easy to show that relation (6) is also valid for pyramids, prisms, and other polyhedra. Euler was the first to recognize and prove this important property of polyhedra.