A polyhedron is said to be regular if it satisifies:
- All it's faces are regular polygons;
- The same sequence of polygons surrounds each vertex.
It may be shown that there are just five convex regular polyhedra. These are known as the Platonic Solids. If star faces and/or vertices are permitted, then four more regular polyhedra can be added to this total. These four, which were unknown to the ancient world, are known as the Kepler-Poinsot Star Polyhedra.
See Also: Semi-Regular Polyhedron.