Small snubspinosnub prismatosnub trishexacosichoron

Small snubspinosnub prismatosnub trishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sosanspistax
Elements
Cells	600 great icosahedra, 2400 compound of cuboctahedron and cubohemioctahedron, 120 icosidisicosahedra, 600 small ditrigonal dodecicosidodecahedra, 600 rhombicosahedra, 3600 pentagrammic prisms
Faces	21600 triangles, 32400 squares, 7200 pentagrams, 10800 hexagons, 1200 golden hexagrams, 3600 decagons, 600 compound of two hexagons
Edges	14400+2×21600
Vertices	7200
Measures (edge length 1)
Circumradius	${\sqrt {4+{\sqrt {5}}}}\approx 2.49721$
Related polytopes
Army	Semi-uniform Prahi
Regiment	Sadros daskydox
Conjugate	Gosanspistax
Abstract & topological properties
Euler characteristic	18000
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small snubspinosnub prismatosnub trishexacosichoron, or sosanspistax, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 2400 cuboctahedra and 2400 cubohemioctahedra (some of which lie in the same hyperplanes, forming 2400 compounds of one of each), 600 octahemioctahedra (forming 120 icosidisicosahedra), 600 small ditrigonal dodecicosidodecahedra, 600 rhombicosahedra, and 3600 pentagrammic prisms.

One great icosahedron, four cuboctahedra and four cubohemioctahedra (eight compounds), one octahemioctahedron (one compound), five small ditrigonal dodecicosidodecahedra, five rhombicosahedra, and five pentagrammic prisms join at each vertex.

It can be obtained as the blend of 5 small dipentary hexacosiprismatodishecatonicosachora and 5 small dipentary hexacosihecatonicosachora. In the process, some of the cuboctahedron and cubohemioctahedron cells blend out.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small diretrosnub disnub decahecatonicosadishexacosichoron.

External links

• Bowers, Jonathan. "Category 28: Idcossids" (#1663).