Regular icosahedron Regular icosahedron In geometry, a regular icosahedron ( or ) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most sides. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol {3,5}, or sometimes by its vertex figure as 3.3.3.3.3 or 3. It is the dual of the dodecahedron, which is represented by {5,3}, having three pentagonal faces around each vertex. A regular icosahedron is a gyroelongated pentagonal bipyramid and a biaugmented pentagonal antiprism in any of
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