Regular dodecahedron dodecahedron forms an icosidodecahedron. The regular dodecahedron has icosahedral symmetry I, Coxeter group [5,3], order 120, with an abstract group structure of "A" × "Z". When a regular dodecahedron is inscribed in a sphere, it occupies more of the sphere's volume (66.49%) than an icosahedron inscribed in the same sphere (60.54%). A regular dodecahedron with edge length 1 has more than three and a half times the volume of an icosahedron with the same length edges (7.663... compared with 2.181...), which ratio is approximately , or in exact terms: or . A regular dodecahedron has 12 faces and 20 vertices,
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"