Platonic Solids

Platonic Solid — from Wolfram MathWorld.

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convexregular polygons. There are exactly five such solids (Steinhaus 1999, pp. 252-256): the cubedodecahedronicosahedronoctahedron, and tetrahedron, as was proved by Euclid in the last proposition of the Elements. The Platonic solids are sometimes also called “cosmic figures” (Cromwell 1997), although this term is sometimes used to refer collectively to both the Platonic solids and Kepler-Poinsot solids (Coxeter 1973).