A number of attractive dodecahedron 2-compounds are illustrated above.

A compound of two dodecahedra having the symmetry of the cube arises by combining two dodecahedra rotated with respect to each other about a common axis (Holden 1991, p. 37). This compound is implemented in Mathematica as PolyhedronData["DodecahedronTwoCompound"].

The compound can be constructed from the net above. For dodecahedra with unit edge lengths, the side lengths are

			(1)
			(2)
			(3)
			(4)

where is the golden ratio. The surface area of the compound is

(5)

Holden, A. Shapes, Space, and Symmetry. New York: Dover, p. 37, 1991.

CITE THIS AS:

Weisstein, Eric W. "Dodecahedron 2-Compound." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Dodecahedron2-Compound.html