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
Regular dodecahedron dodecahedra were made and have been found in various Roman ruins in Europe. Their purpose is not certain. In 20th-century art, dodecahedra appear in the work of M. C. Escher, such as his lithographs "Reptiles" (1943) and "Gravitation" (1952). In Salvador Dalí's painting "The Sacrament of the Last Supper" (1955), the room is a hollow regular dodecahedron. Gerard Caris based his entire artistic oeuvre on the regular dodecahedron and the pentagon, which is presented as a new art movement coined as Pentagonism. In modern role-playing games, the regular dodecahedron is often used as a twelve-sided die, one of the more