Small ditetrahedronary prismatocubihexacosichoron

Small ditetrahedronary prismatocubihexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSidtapicax
Elements
Cells600 tetrahedra, 1200 triangular prisms, 120 compounds of five cubes
Faces2400 triangles, 3600 squares
Edges3600
Vertices600
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 25{\frac {46+25{\sqrt {5}}}{4}}\approx 636.88562}$
Dichoral anglesTrip–4–cube: ${\displaystyle \arccos \left(-{\frac {{\sqrt {3}}+{\sqrt {15}}}{6}}\right)\approx 159.09484^{\circ }}$
Tet–3–trip: ${\displaystyle \arccos \left({\frac {{\sqrt {6}}+{\sqrt {30}}}{8}}\right)\approx 7.76124^{\circ }}$
Number of external pieces96120
Level of complexity190
Related polytopes
ArmyHi, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSidtaxhi
ConjugateGrand ditetrahedronary prismatocubihexacosichoron
Abstract & topological properties
Flag count86400
Euler characteristic600
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

The small ditetrahedronary prismatocubihexacosichoron, or sidtapicax, is a nonconvex uniform polychoron that consists of 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 600 tetrahedra, and 1200 triangular prisms. Eight cubes (or four compounds), four tetrahedra, 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.