Great retrofrustary tetracontoctitetrisicositetrachoron

Great retrofrustary tetracontoctitetrisicositetrachoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Girfcuti
Elements
Cells	48 co, 24 groh, 24 socco, 24 sirco, 24 cotco
Faces	384 triangles, 576 squares, 96 hexagons, 144 octagons, 144 octagrams
Edges	576+576
Vertices	288
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Related polytopes
Army	Cont
Regiment	Afdec
Conjugate	Sifcuti
Abstract & topological properties
Euler characteristic	336
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Wild

The great retrofrustary tetracontoctitetrisicositetrachoron, or girfcuti, is a nonconvex uniform polychoron that consists of 48 cuboctahedra, 24 great rhombihexahedra, 24 small cubicuboctahedra, 24 small rhombicuboctahedra, and 24 cuboctatruncated cuboctahedra. Two cuboctahedra, two great rhombihexahedra, two small cubicuboctahedra, two small rhombicuboctahedra, and four cuboctatruncated cuboctahedra join at each vertex.

It has the same cell counts as the small retrofrustary tetracontoctitetrisicositetrachoron, but the great rhombihexahedra, small cubicuboctahedra, and small rhombicuboctahedra are in different positions.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the antifrustary distetracontoctachoron.

External links

• Bowers, Jonathan. "Category 15: Afdec Regiment" (#645).