Small dispinosnub prismatosnub hexishexacosichoron

Small dispinosnub prismatosnub hexishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sednaspishax
Elements
Cells	600 pentagrammatic snub pseudodisoctahedra, 600 great dodecahedra, 2400 compound of two cubohemioctahedra, 600 rhombidodecadodecahedra, 600 compound of two small dodecicosahedra, 3600 pentagrammic prisms
Faces	32400 squares, 7200 pentagons, 14400 pentagrams, 14400 hexagons, 3600 compound of two hexagons, 7200 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	Gednaspishax
Abstract & topological properties
Euler characteristic	20400
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small dispinosnub prismatosnub hexishexacosichoron, or sednaspishax, is a nonconvex uniform polychoron that consists of 1200 small stellated dodecahedra (some of which lie in the same hyperplanes, forming 600 pentagrammatic snub pseudodisoctahedra), 600 great dodecahedra, 4800 cubohemioctahedra (forming 2400 compounds of two), 600 rhombidodecadodecahedra, 1200 small dodecicosahedra (forming 600 compounds of two), and 3600 pentagrammic prisms.

Two small stellated dodecahedra (two compounds), one great dodecahedron, eight cubohemioctahedra (eight compounds), five rhombidodecadodecahedra, ten small dodecicosahedra (ten compounds), and five pentagrammic prisms join at each vertex.

It can be obtained as the blend of 5 small capped dipentary tetrishecatonicosihexacosichora and 5 small dipentary hecatonicosiprismatohecatonicosihexacosichora. 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" (#1564).