Small snub icosicosidodecahedron = (1+)/2 is the golden ratio and α = . 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
Regular dodecahedron The dodecahedra alone make a lattice of edge-to-edge pyritohedra. The bilunabirotundae fill the rhombic gaps. Each cube meets six bilunabirotundae in three orientations. The regular dodecahedron is topologically related to a series of tilings by vertex figure "n". The regular dodecahedron can be transformed by a truncation sequence into its dual, the icosahedron: The regular dodecahedron is a member of a sequence of otherwise non-uniform polyhedra and tilings, composed of pentagons with face configurations (V3.3.3.3."n"). (For "n" > 6, the sequence consists of tilings of the hyperbolic plane.) These face-transitive figures have ("n"32) rotational symmetry. The regular dodecahedron shares its