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
Trapezo-rhombic dodecahedron optimal way to stack spheres. As the Voronoi cell of a regular space pattern, it is a plesiohedron. It is the polyhedral dual of the triangular orthobicupola. The "trapezo-rhombic dodecahedron" can be seen as an elongation of another dodecahedron, which can be called a rhombo-triangular dodecahedron, with 6 rhombi (or squares) and 6 triangles. It also has d symmetry and is space-filling. It has 21 edges and 11 vertices. With square faces it can be seen as a cube split across the 3-fold axis, separated with the two halves rotated 180 degrees, and filling the gaps with triangles. When used