Small retrotetracontoctachoron

Small retrotetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sirc
Elements
Cells	48 small rhombihexahedra
Faces	288 squares, 144 octagons
Edges	576
Vertices	144
Vertex figure	Square stephanoid, edge lengths √2 and √2+√2
Edge figure	sroh 4 sroh 8 sroh 4 sroh 8
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Inradius	${\frac {1+{\sqrt {2}}}{2}}\approx 1.20711$
Dichoral angles	Sroh–8–sroh: 135°
	Sroh–4–sroh: 90°
Number of external pieces	2736
Level of complexity	40
Related polytopes
Army	Spic
Regiment	Spic
Conjugate	Great retrotetracontoctachoron
Abstract & topological properties
Flag count	9216
Euler characteristic	–48
Orientable	No
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

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

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

External links

• Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#519).

• Klitzing, Richard. "sirc".