Small dispinosnub heptishexacosichoron

Small dispinosnub heptishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sednashox
Elements
Cells	600 small stellated dodecahedra, 600 pentagonal retrosnub pseudodisoctahedra, 2400 compound of two cubohemioctahedra, 600 rhombidodecadodecahedra, 600 small dodecicosahedra, 600 small rhombidodecahedra, 600 truncated icosahedra
Faces	32400 squares, 14400 pentagons, 7200 pentagrams, 19200 hexagons, 1200 compound of two hexagons, 3600 decagons
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	Gednashox
Abstract & topological properties
Euler characteristic	19800
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small dispinosnub heptishexacosichoron, or sednashox, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra, 1200 great dodecahedra (some of which lie in the same hyperplanes, forming 600 pentagonal retrosnub pseudodisoctahedra), 4800 cubohemioctahedra (forming 2400 compounds of two), 600 rhombidodecadodecahedra, 600 small dodecicosahedra, 600 small rhombidodecahedra, and 600 truncated icosahedra.

One small stellated dodecahedron, two great dodecahedra (two compounds), eight cubohemioctahedra (eight compounds), five rhombidodecadodecahedra, five small dodecicosahedra, five small rhombidodecahedra, and five truncated icosahedra join at each vertex.

It can be obtained as the blend of 5 small capped dipentary tetrishecatonicosihexacosichora and 5 small spinobased dipentary hexacositrishecatonicosachora. 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" (#1562).