Truncated dodecahedron Truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb. The area "A" and the volume "V" of a truncated dodecahedron of edge length "a" are: Cartesian coordinates for the vertices of a truncated dodecahedron with edge length 2"φ" − 2, centered at the origin, are
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"