Small ditetrahedronary cubiprismatohecatonicosachoron

Small ditetrahedronary cubiprismatohecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidtacphi
Elements
Cells	120 compounds of five cubes, 120 dodecahedra, 720 pentagonal prisms
Faces	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	32520
Level of complexity	79
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Gadtacphi
Abstract & topological properties
Flag count	86400
Euler characteristic	600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small ditetrahedronary cubiprismatohecatonicosachoron, or sidtacphi, is a nonconvex uniform polychoron that consists of 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 120 dodecahedra, and 720 pentagonal prisms. Eight cubes (or four compounds), four dodecahedra, and twelve pentagonal prisms 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" (#788).