Great rhombiprismic hecatonicosihexacosichoron

Great rhombiprismic hecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Griphix
Elements
Cells	1200 hexagonal prisms, 600 truncated octahedra, 120 rhombicosahedra
Faces	3600+3600 squares, 2400+2400 hexagons
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Butterfly pyramid, base edge lengths √2, √3, √2, √3; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\sqrt {17-6{\sqrt {5}}}}\approx 1.89304$
Dichoral angles	Toe–6–hip: $\arccos \left({\frac {{\sqrt {6}}-{\sqrt {30}}}{8}}\right)\approx 112.23876^{\circ }$
	Ri–4–hip: $\arccos \left({\frac {{\sqrt {3}}-{\sqrt {15}}}{6}}\right)\approx 110.90516^{\circ }$
	Ri–6–toe: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Toe–4–hip: $\arccos \left({\frac {\sqrt {30}}{6}}\right)\approx 24.09484^{\circ }$
Related polytopes
Army	Semi-uniform Prix
Regiment	Pirgaghi
Conjugate	Small rhombiprismic hecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	–720
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great rhombiprismic hecatonicosihexacosichoron, or griphix, is a nonconvex uniform polychoron that consists of 120 rhombicosahedra, 600 hexagonal prisms, and 1200 truncated octahedra. One rhombicosahedron, two hexagonal prisms, and two truncated octahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the prismatorhombated great grand hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#378).