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,
Rhombic dodecahedron The "rhombic dodecahedron" has four special orthogonal projections along its axes of symmetry, centered on a face, an edge, and the two types of vertex, threefold and fourfold. The last two correspond to the B and A Coxeter planes. The eight vertices where three faces meet at their obtuse angles have Cartesian coordinates: The coordinates of the six vertices where four faces meet at their acute angles are: The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates and with parameter "h" = 1. The "rhombic dodecahedron" is a parallelohedron, a space-filling