Grand rhombic small hecatonicosihexacosichoron

Grand rhombic small hecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Garshix
Elements
Cells	600 truncated octahedra, 120 rhombicosahedra
Faces	3600 squares, 1200+2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Crossed butterfly wedge, edge lengths √2 (4) and √3 (6)
Measures (edge length 1)
Circumradius	${\sqrt {7+2{\sqrt {5}}}}\approx 3.38705$
Dichoral angles	Ri–6–toe: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Toe–6–toe: $\arccos \left({\frac {1-3{\sqrt {5}}}{8}}\right)\approx 135.52249^{\circ }$
	Ri–4–toe: 135°
Related polytopes
Army	Semi-uniform Srix, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (icosidodecahedra), ${\frac {3-{\sqrt {5}}}{2}}$ (main triangles)
Regiment	Sirghi
Conjugate	Grand rhombic great hecatonicosihexacosichoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–720
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The grand rhombic small hecatonicosihexacosichoronn, or garshix, is a nonconvex uniform polychoron that consists of 120 rhombicosahedra and 600 truncated octahedra. Two rhombicosahedra and four truncated octahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated great hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#190).