Dodecahedron dodecahedron has several stellations, the first of which is also a parallelohedral spacefiller. Another important rhombic dodecahedron, the Bilinski dodecahedron, has twelve faces congruent to those of the rhombic triacontahedron, i.e. the diagonals are in the ratio of the golden ratio. It is also a zonohedron and was described by Bilinski in 1960. This figure is another spacefiller, and can also occur in non-periodic spacefillings along with the rhombic triacontahedron, the rhombic icosahedron and rhombic hexahedra. There are 6,384,634 topologically distinct "convex" dodecahedra, excluding mirror images—the number of vertices ranges from 8 to 20. (Two polyhedra are "topologically distinct" if
Snub dodecahedron of snubbed polyhedra and tilings with vertex figure (3.3.3.3."n") and Coxeter–Dynkin diagram . These figures and their duals have ("n"32) rotational symmetry, being in the Euclidean plane for "n" = 6, and hyperbolic plane for any higher "n". The series can be considered to begin with "n" = 2, with one set of faces degenerated into digons. In the mathematical field of graph theory, a snub dodecahedral graph is the graph of vertices and edges of the snub dodecahedron, one of the Archimedean solids. It has 60 vertices and 150 edges, and is an Archimedean graph. Snub dodecahedron In geometry,