Small snub icosicosidodecahedron

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}.

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.

be largest (least negative) zero of the polynomial

be the transformations which send a point

with an even number of minus signs.

constitute the group of rotational symmetries of a regular tetrahedron.

constitute the group of rotational symmetries of a regular icosahedron.

are the vertices of a small snub icosicosidodecahedron.

The edge length equals

, and the midradius equals

For a small snub icosicosidodecahedron whose edge length is 1, the circumradius is Its midradius is The other zero of

plays a similar role in the description of the small retrosnub icosicosidodecahedron.

This polyhedron-related article is a stub.