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,
Truncated dodecahedron straight edges. It shares its vertex arrangement with three nonconvex uniform polyhedra: It is part of a truncation process between a dodecahedron and icosahedron: This polyhedron is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2"n".2"n"), and ["n",3] Coxeter group symmetry. In the mathematical field of graph theory, a truncated dodecahedral graph is the graph of vertices and edges of the "truncated dodecahedron", one of the Archimedean solids. It has 60 vertices and 90 edges, and is a cubic Archimedean graph. Truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has