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See also: Regular Polyhedra 

Dodecahedron

A regular dodecahedron is one of the Platonic solids, having 12 regular pentagonal faces.

The coordinates of the vertices of a dodecahedron can be described by the following two expressions:

where k=0..4, and F is the Golden Ratio . The top and bottom faces of this dodecahedron are in parallel to the xy-plane, the edge length is .

The volume V of the dodecahedron with given edge length a is

its surface S is

The radii of the circumscribed (rc) and inscribed (ri) spheres are

= a1.40125853844407354467...,
and
= a1.11351636441160673519...

Last Update: 2007-Sep-03