Excavated dodecahedron Excavated dodecahedron In geometry, the excavated dodecahedron is a star polyhedron having 60 equilateral triangular faces. Its exterior surface represents the Efg stellation of the icosahedron. It appears in Magnus Wenninger's book "Polyhedron Models" as model 28, the "third stellation of icosahedron". It has the same external form as a certain facetting of the dodecahedron having 20 self-intersecting hexagons as faces. The non-convex hexagon face can be broken up into four equilateral triangles, three of which are the same size. A true excavated dodecahedron has the three congruent equilateral triangles as true faces of the polyhedron, while the interior equilateral
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