Small retrotetracontoctachoron

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Small retrotetracontoctachoron
Rank4
TypeUniform
Notation
Bowers style acronymSirc
Elements
Cells48 small rhombihexahedra
Faces288 squares, 144 octagons
Edges576
Vertices144
Vertex figureSquare stephanoid, edge lengths 2 and 2+2
Edge figuresroh 4 sroh 8 sroh 4 sroh 8
Measures (edge length 1)
Circumradius
Inradius
Dichoral anglesSroh–8–sroh: 135°
 Sroh–4–sroh: 90°
Number of external pieces2736
Level of complexity40
Related polytopes
ArmySpic
RegimentSpic
ConjugateGreat retrotetracontoctachoron
Abstract & topological properties
Flag count9216
Euler characteristic–48
OrientableNo
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

The small retrotetracontoctachoron, or sirc, is a nonconvex noble uniform polychoron that consists of 48 small rhombihexahedra. Eight cells join at each vertex.

It can be constructed as a blend of 9 octagonal duoprisms, with the small rhombihexahedra being blends of 3 octagonal prisms. It can also be seen as the blend of 3 grand rhombic prismatotesseracts, each of which is a blend of 3 octagonal duoprisms.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small prismatotetracontoctachoron.

External links[edit | edit source]