The Platonic Solids

A polyhedron is said to be regular if it satisfies:

  1. All its faces are regular polygons having the same number, p, of edges;
  2. The sames number, q, of these polygons meet at each vertex.

It can be shown that there are exactly five convex regular polyhedra, which are colectively know as the Platonic Solids. They are the regular versions of the following polyhedra:

See Also: Kepler Poinsot Star Polyhedra.