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
Bilinski dodecahedron affine transformation from the rhombic dodecahedron, but this is false. For, in the Bilinski dodecahedron, the long body diagonal is parallel to the short diagonals of two faces, and to the long diagonals of two other faces. In the rhombic dodecahedron, the corresponding body diagonal is parallel to four short face diagonals, and in any affine transformation of the rhombic dodecahedron this body diagonal would remain parallel to four equal-length face diagonals. Another difference between the two dodecahedra is that, in the rhombic dodecahedron, all the body diagonals connecting opposite degree-4 vertices are parallel to face diagonals, while in the