Small dispinosnub prismatodisnub hexishexacosichoron

Small dispinosnub prismatodisnub hexishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidnaspidshox
Elements
Cells	600 small stellated dodecahedra, 600 compound of great dodecahedron and icosahedron, 2400 compound of two cubohemioctahedra, 600 rhombidodecadodecahedra, 600 compound of two small dodecicosahedra, 6000 triangular prisms
Faces	12000 triangles, 32400 squares, 7200 pentagons, 7200 pentagrams, 14400 hexagons, 7200 decagons, 3600 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	Gidnaspidshox
Abstract & topological properties
Euler characteristic	22800
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small dispinosnub prismatodisnub hexishexacosichoron, or sidnaspidshox, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra, 600 great dodecahedra and 600 icosahedra (some of which lie in the same hyperplanes, forming 600 compounds of one of each), 4800 cubohemioctahedra (forming 2400 compounds of two), 600 rhombidodecadodecahedra, 1200 small dodecicosahedra (forming 600 compounds of two), and 6000 triangular prisms.

One small stellated dodecahedron, one great dodecahedron and one icosahedron (two compounds), eight cubohemioctahedra (eight compounds), five rhombidodecadodecahedra, ten small dodecicosahedra (ten compounds), and five triangular prisms join at each vertex.

It can be obtained as the blend of 5 small capped dipentary tetrishecatonicosihexacosichora and 5 small dipentary hecatonicosiprismatohexacosihecatonicosachora. In the process, some of the 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" (#1586).