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,
Dodecahedron of the wedge-shaped "roof" above the faces of the cube. When "h" = 1, the six cross-edges degenerate to points and a rhombic dodecahedron is formed. When "h" = 0, the cross-edges are absorbed in the facets of the cube, and the pyritohedron reduces to a cube. When "h" = , the multiplicative inverse of the golden ratio, the result is a regular dodecahedron. When "h" = , the conjugate of this value, the result is a regular great stellated dodecahedron. A reflected pyritohedron is made by swapping the nonzero coordinates above. The two pyritohedra can be superimposed to give