The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.


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 Φ 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...,
= a1.11351636441160673519...

Last Update: 2011-01-11