Regular icosahedron Regular icosahedron In geometry, a regular icosahedron ( or ) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most sides. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol {3,5}, or sometimes by its vertex figure as 3.3.3.3.3 or 3. It is the dual of the dodecahedron, which is represented by {5,3}, having three pentagonal faces around each vertex. A regular icosahedron is a gyroelongated pentagonal bipyramid and a biaugmented pentagonal antiprism in any of
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"