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
Snub dodecahedron Snub dodecahedron In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces. The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two snub dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron. Kepler