Small ditetrahedronary prismatocubidishecatonicosachoron

Small ditetrahedronary prismatocubidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sadtipacady
Elements
Cells	120 compounds of five cubes, 120 dodecahedra, 120 icosidodecahedra, 1200 triangular prisms
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	104520
Level of complexity	208
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Gadtapacady
Abstract & topological properties
Flag count	115200
Euler characteristic	2400
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small ditetrahedronary prismatocubidishecatonicosachoron, or sadtipacady, is a nonconvex uniform polychoron that consists of 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 120 dodecahedra, 120 icosidodecahedra, and 1200 triangular prisms. Eight cubes (or four compounds), four dodecahedra, six icosidodecahedra, and twelve triangular 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" (#790).