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

Home Analytic Geometry 3D Solids Platonic Solids Dodecahedron
See also: Platonic Solids - Regular Polyhedra 
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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 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...,
and
= a1.11351636441160673519...
Home Analytic Geometry 3D Solids Platonic Solids Dodecahedron

Last Update: 2011-01-11