Small snubretrosnub hexishexacosichoron

Small snubretrosnub hexishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sosershox
Elements
Cells	600 small retrosnub disoctahedra, 600 snub disoctahedra, 2400 compound of octahemioctahedron and cuboctahedron, 120 great antirhombicosahedra, 600 small rhombidodecahedra, 600 small dodecicosahedra
Faces	28800 triangles, 18000 squares, 10800 hexagons, 7200 golden hexagrams, 7200 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	Gosershox
Abstract & topological properties
Euler characteristic	21000
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small snubretrosnub hexishexacosichoron, or sosershox, is a nonconvex uniform polychoron that consists of 1200 great icosahedra (some of which lie in the same hyperplanes, forming 600 small retrosnub disoctahedra), 1200 icosahedra (forming 600 snub disoctahedra), 2400 octahemioctahedra and 2400 cuboctahedra (forming 2400 compounds of one of each), 600 cubohemioctahedra (forming 120 great antirhombicosahedra), 600 small rhombidodecahedra, and 600 small dodecicosahedra.

Two great icosahedra (two compounds), two icosahedra (two compounds), four octahemioctahedra and four cuboctahedra (eight compounds), one cubohemioctahedron (one compound), five small rhombidodecahedra, and five small dodecicosahedra join at each vertex.

It can be obtained as the blend of 5 small dipentary hecatonicosihexacosidishecatonicosachora and 5 small dipentary dishecatonicosihexacosihecatonicosachora. In the process, some of the octahemioctahedron and cuboctahedron 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" (#1615).