Small snub icosicosidodecahedron


In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. It has 112 faces, 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß.
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.

Convex hull

Its convex hull is a nonuniform truncated icosahedron.

Truncated icosahedron

Convex hull

Small snub icosicosidodecahedron

Cartesian coordinates

for the vertices of a small snub icosicosidodecahedron are all the even permutations of
where ϕ = /2 is the golden ratio and α =.