Small disnub hexacosihexacosihexacosichoron

Small disnub hexacosihexacosihexacosichoron
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidsaxixox
Elements
Cells	600 great dodecahedra, 600 truncated dodecahedra, 600 small rhombicosidodecahedra, 2400 golden hexagrammic antiprisms
Faces	12000+14400 triangles, 9000 squares, 7200 pentagons, 2400 golden hexagrams, 3600 decagons
Edges	7200+7200+14400
Vertices	3600
Measures (edge length 1)
Circumradius	$\sqrt{5+2\sqrt5} ≈ 3.07768$
Related polytopes
Army	Semi-uniform Srix
Regiment	Sadsadox
Conjugate	Gidsaxixox
Abstract & topological properties
Euler characteristic	19200
Orientable	Yes
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small disnub hexacosihexacosihexacosichoron, or sidsaxixox, is a nonconvex uniform polychoron that consists of 600 great dodecahedra, 600 truncated dodecahedra, 600 small rhombicosidodecahedra, and 4800 octahedra (some of which lie in the same hyperplanes, forming 2400 golden hexagrammic antiprisms). Two great dodecahedra, ten truncated dodecahedra, ten small rhombicosidodecahedra, and eight octahedra (eight compounds) join at each vertex.

It can be obtained as the blend of 5 rixhi and 5 nipixady. In the process, some of the octahedron cells blend out.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small disnub dishexacosichoron.

External links

• Bowers, Jonathan. "Category 27: Sidtaps and Gidtaps" (#1481).