There are two distinct convex golden rhombohedra constructed from six golden rhombi as a trigonal trapezohedron. These are sometimes called acute or prolate and the obtuse or oblate golden rhombohedron.
The rhombic triacontahedron is constructed with 30 golden rhombic faces, alternating 3 and 5 around every vertex. The dihedral angle between adjacent rhombi of the rhombic triacontahedron is 144°, which can be constructed by placing the short sides of two golden triangles back-to-back. The rhombic icosahedron is also constructed with golden rhombi.
The internal angles of the rhombus are
The edge length of the golden rhombus with short diagonal is
A golden rhombus with unit edge length has diagonal lengths
- M. Livio, The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, New York: Broadway Books, p. 206, 2002.
- Weisstein, Eric W., "Golden Rhombus", MathWorld.
- Weisstein, Eric W., "Golden Rhombohedron", MathWorld.