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In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. 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}.
Contents
The 40 non-sub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.
Convex hull
Its convex hull is a nonuniform truncated icosahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of a small snub icosicosidodecahedron are all the even permutations of
(±(1-ϕ+α), 0, ±(3+ϕα))(±(ϕ-1+α), ±2, ±(2ϕ-1+ϕα))(±(ϕ+1+α), ±2(ϕ-1), ±(1+ϕα))where ϕ = (1+√5)/2 is the golden ratio and α = √(3ϕ−2).
References
Small snub icosicosidodecahedron Wikipedia(Text) CC BY-SA