** Next:** 13.2 Cylinders
**Up:** 13 Polyhedra
** Previous:** 13 Polyhedra

Figure 1 shows the five regular polyhedra, or
**Platonic solids**.

**Figure 1:** The Platonic solids.
Top: the tetrahedron (self-dual).
Middle: the cube and the octahedron (dual to one another).
Bottom: the dodecahedron and the icosahedron (dual to one another).

In the following tables and formulas, *a* is
the length of an edge, the dihedral angle at each edge, *R*
the radius of the circumscribed sphere, *r* the radius of the
inscribed sphere, *V* the volume, *S* the total area, *v* the total
number of vertices, *e* the total number of edges, *f* the total
number of faces, *p* the number of edges in a face, and *q* the number
of edges meeting at a vertex.

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.