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
Rhombic dodecahedron The "rhombic dodecahedron" has four special orthogonal projections along its axes of symmetry, centered on a face, an edge, and the two types of vertex, threefold and fourfold. The last two correspond to the B and A Coxeter planes. The eight vertices where three faces meet at their obtuse angles have Cartesian coordinates: The coordinates of the six vertices where four faces meet at their acute angles are: The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates and with parameter "h" = 1. The "rhombic dodecahedron" is a parallelohedron, a space-filling