Quasirhombated great grand stellated hecatonicosachoron

Quasirhombated great grand stellated hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Qrigogishi
Coxeter diagram	x5/3o3x3o ()
Elements
Cells	600 octahedra, 1200 triangular prisms, 120 quasirhombicosidodecahedra
Faces	2400+2400 triangles, 3600 squares, 720 pentagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Crossed wedge, edge lengths 1 (base square), √2 (side edges), and (√5–1)/2 (top edge)
Measures (edge length 1)
Circumradius	${\sqrt {23-10{\sqrt {5}}}}\approx 0.79958$
Hypervolume	$5{\frac {1870-823{\sqrt {5}}}{2}}\approx 74.29014$
Dichoral angles	Qrid–3–oct: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Qrid–5/2–qrid: 72°
	Qrid–4–trip: $\arccos \left({\frac {{\sqrt {15}}-{\sqrt {3}}}{6}}\right)\approx 69.09484^{\circ }$
	Oct–3–trip: $\arccos \left({\frac {{\sqrt {30}}-{\sqrt {6}}}{8}}\right)\approx 67.76124^{\circ }$
Related polytopes
Army	Semi-uniform Srix
Regiment	Gwavixady
Conjugate	Small rhombated hecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The quasirhombated great grand stellated hecatonicoscahoron, or qrigogishi, is a nonconvex uniform polychoron that consists of 600 regular octahedra, 1200 triangular prisms, and 120 quasirhombicosidodecahedra. 1 octahedron, 2 triangular prisms, and 2 quasirhombicosidodecahedra join at each vertex. It can be obtained by quasicantellating the great grand stellated hecatonicosachoron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great sphenoverted hexacosidishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#285).

• Klitzing, Richard. "qrigogishi".