Excavated dodecahedron triangle is not present. The 20 vertices of the convex hull match the vertex arrangement of the dodecahedron. The faceting is a noble polyhedron. With six six-sided faces around each vertex, it is topologically equivalent to a quotient space of the hyperbolic order-6 hexagonal tiling, {6,6} and is an abstract type {6,6}. It is one of ten abstract regular polyhedra of index two with vertices on one orbit. 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
Regular dodecahedron the children's novel "The Phantom Tollbooth", the regular dodecahedron appears as a character in the land of Mathematics. Each of his faces wears a different expression – "e.g." happy, angry, sad – which he swivels to the front as required to match his mood. Dodecahedron is the name of an avant-garde black metal band from Netherlands. Various models have been proposed for the global geometry of the universe. In addition to the primitive geometries, these proposals include the Poincaré dodecahedral space, a positively curved space consisting of a regular dodecahedron whose opposite faces correspond (with a small twist). This was