## Platonic Solids

#### Problem

It is well known that the five Platonic solids are the regular tetrahedron (four equilateral triangle faces), cube (six square faces), regular octahedron (eight equilateral triangle faces), regular dodecahedron (twelve regular pentagon faces), and the regular icosahedron (twenty equilateral triangle faces).

Prove that no more than five regular (convex) polyhedra exist.

Problem ID: 246 (28 Oct 2005) Difficulty: 3 Star