# Grand rhombic small hecatonicosihexacosichoron

Grand rhombic small hecatonicosihexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymGarshix
Elements
Cells600 truncated octahedra, 120 rhombicosahedra
Faces3600 squares, 1200+2400 hexagons
Edges3600+7200
Vertices3600
Vertex figureCrossed butterfly wedge, edge lengths 2 (4) and 3 (6)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {7+2{\sqrt {5}}}}\approx 3.38705}$
Dichoral anglesRi–6–toe: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }}$
Toe–6–toe: ${\displaystyle \arccos \left({\frac {1-3{\sqrt {5}}}{8}}\right)\approx 135.52249^{\circ }}$
Ri–4–toe: 135°
Related polytopes
ArmySemi-uniform Srix, edge lengths ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$ (icosidodecahedra), ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$ (main triangles)
RegimentSirghi
ConjugateGrand rhombic great hecatonicosihexacosichoron
Abstract & topological properties
Flag count144000
Euler characteristic–720
OrientableNo
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

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.