Dodecahedron regular dodecahedron but less symmetrical: the pyritohedron with pyritohedral symmetry, and the tetartoid with tetrahedral symmetry: A pyritohedron is a dodecahedron with pyritohedral (T) symmetry. Like the regular dodecahedron, it has twelve identical pentagonal faces, with three meeting in each of the 20 vertices. However, the pentagons are not constrained to be regular, and the underlying atomic arrangement has no true fivefold symmetry axes. Its 30 edges are divided into two sets – containing 24 and 6 edges of the same length. The only axes of rotational symmetry are three mutually perpendicular twofold axes and four threefold axes. Although regular
Truncated great dodecahedron a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces. Truncated great dodecahedron In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U. It is given a Schläfli symbol t{5,5/2}. It shares its vertex arrangement with three other uniform polyhedra: the nonconvex great rhombicosidodecahedron, the great dodecicosidodecahedron, and the great rhombidodecahedron; and with the uniform compounds of 6 or 12 pentagonal prisms. This polyhedron is the truncation of the great dodecahedron: The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24