Small ditetrahedronary cubihexacosidishecatonicosachoron

Small ditetrahedronary cubihexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sadticaxady
Elements
Cells	120 compounds of five cubes, 600 tetrahedra, 120 dodecahedra, 120 small rhombicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagons
Edges	3600
Vertices	600
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} \approx 2.28825$
Number of external pieces	117720
Level of complexity	232
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Gadtacaxady
Abstract & topological properties
Flag count	115200
Euler characteristic	3000
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small ditetrahedronary cubihexacosidishecatonicosachoron, or sadticaxady, is a nonconvex uniform polychoron that consists of 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 600 tetrahedra, 120 dodecahedra, and 120 small rhombicosidodecahedra. Eight cubes (or four compounds), four tetrahedra, four dodecahedra, and twelve small rhombicosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#796).