Small snub icosicosidodecahedron Small snub icosicosidodecahedron In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}. The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries. Its convex hull is a nonuniform truncated icosahedron. Cartesian coordinates for the vertices of a small snub icosicosidodecahedron are all the even permutations of where ϕ
Dodecahedron of the wedge-shaped "roof" above the faces of the cube. When "h" = 1, the six cross-edges degenerate to points and a rhombic dodecahedron is formed. When "h" = 0, the cross-edges are absorbed in the facets of the cube, and the pyritohedron reduces to a cube. When "h" = , the multiplicative inverse of the golden ratio, the result is a regular dodecahedron. When "h" = , the conjugate of this value, the result is a regular great stellated dodecahedron. A reflected pyritohedron is made by swapping the nonzero coordinates above. The two pyritohedra can be superimposed to give