Small ditetrahedronary prismatohexacosicubihecatonicosachoron

Small ditetrahedronary prismatohexacosicubihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sadtip xachi
Elements
Cells	120 compounds of five cubes, 600 tet, 720 pip, 120 saddid
Faces	2400 triangles, 3600 squares, 1440 pentagons, 720 decagons
Edges	3600
Vertices	600
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} \approx 2.28825$
Number of external pieces	106920
Level of complexity	211
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Gadtapaxchi
Abstract & topological properties
Flag count	144000
Euler characteristic	3120
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small ditetrahedronary prismatohexacosicubihecatonicosachoron, or sadtip xachi, is a nonconvex uniform polychoron that consists of 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 600 tetrahedra, 720 pentagonal prisms, and 120 small dodecicosidodecahedra. Eight cubes (or four compounds), four tetrahedra, twelve pentagonal prisms, and twelve small dodecicosidodecahedra 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" (#802).