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
Distance-regular graph graphs with any given eigenvalue multiplicity formula_56 (with the exception of the complete multipartite graphs). The cubic distance-regular graphs have been completely classified. The 13 distinct cubic distance-regular graphs are K (or tetrahedron), K, the Petersen graph, the cube, the Heawood graph, the Pappus graph, the Coxeter graph, the Tutte–Coxeter graph, the dodecahedron, the Desargues graph, Tutte 12-cage, the Biggs–Smith graph, and the Foster graph. Distance-regular graph In mathematics, a distance-regular graph is a regular graph such that for any two vertices "v" and "w", the number of vertices at distance "j" from "v" and at distance "k" from "w"