Small retrosnub icosicosidodecahedron

In geometry, the small retrosnub icosicosidodecahedron (also known as a retrosnub disicosidodecahedron, small inverted retrosnub icosicosidodecahedron, or retroholosnub icosahedron) is a nonconvex uniform polyhedron, indexed as U72.

It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices.

[1] It is given a Schläfli symbol sr{⁵/₃,³/₂}.

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.

George Olshevsky nicknamed it the yog-sothoth (after the Cthulhu Mythos deity).

[2][3] Its convex hull is a nonuniform truncated dodecahedron.

be the smallest (most negative) zero of the polynomial

is the golden ratio.

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

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 snub icosicosidodecahedron.

This polyhedron-related article is a stub.