# Small ditetrahedronary cubiprismatohecatonicosachoron

Small ditetrahedronary cubiprismatohecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSidtacphi
Elements
Cells720 pentagonal prisms, 120 dodecahedra, 120 compounds of five cubes
Faces3600 squares, 1440 pentagons
Edges3600
Vertices600
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 15{\frac {185+81{\sqrt {5}}}{4}}\approx 1372.95565}$
Dichoral anglesCube–4–pip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }}$
Doe–5–pip: 18°
Number of external pieces32520
Level of complexity79
Related polytopes
ArmyHi, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSidtaxhi
ConjugateGrand ditetrahedronary cubiprismatohecatonicosachoron
Abstract & topological properties
Flag count86400
Euler characteristic600
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

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.