Final stellation of the icosahedron 180 triangular faces, which are the outermost triangular regions in the stellation diagram. These join along 270 edges, which in turn meet at 92 vertices, with an Euler characteristic of 2. The 92 vertices lie on the surfaces of three concentric spheres. The innermost group of 20 vertices form the vertices of a regular dodecahedron; the next layer of 12 form the vertices of a regular icosahedron; and the outer layer of 60 form the vertices of a nonuniform truncated icosahedron. The radii of these spheres are in the ratio When regarded as a three-dimensional solid object with edge lengths
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