Small dispinosnub pentishexacosichoron

Small dispinosnub pentishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidnaspox
Elements
Cells	600 great icosahedra, 600 great dodecahedra, 2400 compound of two cubohemioctahedra, 600 small rhombicosidodecahedra, 600 small dodecicosahedra, 600 rhombicosahedra
Faces	12000 triangles, 32400 squares, 7200 pentagons, 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	Gidnaspox
Abstract & topological properties
Euler characteristic	18600
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small dispinosnub pentishexacosichoron, or sidnaspox, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 600 great dodecahedra, 4800 cubohemioctahedra (some of which lie in the same hyperplanes, forming 2400 compounds of two), 600 small rhombicosidodecahedra, 600 small dodecicosahedra, and 600 rhombicosahedra.

One great icosahedron, one great dodecahedron, eight cubohemioctahedra (eight compounds), five small rhombicosidodecahedra, five small dodecicosahedra, and five rhombicosahedra join at each vertex.

It can be obtained as the blend of 5 small dipentary hexacosihecatonicosachora and 5 small dipentary hexacosihecatonicositrishecatonicosachora. 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" (#1570).