Golden Rhombohedron

A golden rhombohedron is a rhombohedron whose faces consist of congruent golden rhombi. Golden rhombohedra are therefore special cases of a trigonal trapezohedron as well as zonohedra.

There are two distinct golden rhombohedra: the acute golden rhombohedron and obtuse golden rhombohedron. Both are built from six golden rhombi and comprise two of the five golden isozonohedra. These polyhedra are implemented in the Wolfram Language as PolyhedronData["AcuteGoldenRhombohedron"] and PolyhedronData["ObtuseGoldenRhombohedron"], respectively.

The acute and obtuse golden rhombohedra with edge length  both have surface area

(1)

and have volumes

			(2)
			(3)

respectively.

REFERENCES:

Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant, pp. 169 and 171, 2002.

Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, p. 206, 2002.