The rhombic hexecontahedron is a 60-faced polyhedron that can be obtained by stellating the rhombic
triacontahedron by placing a plane along each edge which is perpendicular to
the plane of symmetry in which the edge lies, and taking the solid bounded by these
planes gives a hexecontahedron (Steinhaus 1999). It is therefore a rhombic
triacontahedron stellation. It appears to have been first noted and illustrated
by Unkelbach (1940) as one of 20 finite equilateral polyhedra whose edges lie in
planes of symmetry and whose faces are convex polygons which do not penetrate one
The 60 faces of the rhombic hexecontahedron are golden
rhombi (Kabai 2002, p. 179).
Amazingly, the rhombic hexecontahedron is inferred to exist in nature as the central core of a quasicrystal aggregate of produced by slow solidification (Guyot 1987).
The rhombic hexecontahedron can be constructed by extending the long edges of each rhombic face of the rhombic triacontahedron
to obtain rhombi on either side of the original that are a factor of the golden
larger that the original central rhombus (Kabai 2002, p. 181).
20 golden rhombohedra can be combined to form a solid rhombic hexecontahedron. An addition 180 regular
dodecahedra can be placed face-to-face to lie along the edges of a rhombic hexecontahedron
(Kabai 2011, Fig. 40).