The rhombic hexacontahedron (sometimes spelled “hexecontahedron”) is one of many stellations of the rhombic triacontahedron. Its sixty faces, like the thirty faces of the rhombic triacontahedron, are golden rhombi — rhombi with diagonals in the golden ratio.

The rotating image above was produced using Stella 4d:  Polyhedron Navigator, a program available at www.software3d.com/Stella.php.