Dodecahedron dodecahedron has several stellations, the first of which is also a parallelohedral spacefiller. Another important rhombic dodecahedron, the Bilinski dodecahedron, has twelve faces congruent to those of the rhombic triacontahedron, i.e. the diagonals are in the ratio of the golden ratio. It is also a zonohedron and was described by Bilinski in 1960. This figure is another spacefiller, and can also occur in non-periodic spacefillings along with the rhombic triacontahedron, the rhombic icosahedron and rhombic hexahedra. There are 6,384,634 topologically distinct "convex" dodecahedra, excluding mirror images—the number of vertices ranges from 8 to 20. (Two polyhedra are "topologically distinct" if
Dodecahedron dodecahedra do not exist in crystals, the pyritohedron form occurs in the crystals of the mineral pyrite, and it may be an inspiration for the discovery of the regular Platonic solid form. Note that the true regular dodecahedron can occur as a shape for quasicrystals with icosahedral symmetry, which includes true fivefold rotation axes. Its name comes from one of the two common crystal habits shown by pyrite, the other one being the cube. The coordinates of the eight vertices of the original cube are: The coordinates of the 12 vertices of the cross-edges are: where "h" is the height