Great prismatohecatonicosihecatonicosihexacosichoron

Great prismatohecatonicosihecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Giphihix
Coxeter diagram	x3x3x5o5/3*b ()
Elements
Cells	720 pentagonal prisms, 600 truncated octahedra, 120 truncated great icosahedra, 120 icosidodecadodecahedra
Faces	3600 squares, 1440 pentagons, 1440 pentagrams, 2400+2400 hexagons
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths (1+√5)/2, √3, (√5–1)/2, √3; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\sqrt {17-6{\sqrt {5}}}}\approx 1.89304$
Hypervolume	$15{\frac {419{\sqrt {5}}-25}{4}}\approx 3419.67181$
Dichoral angles	Ided–5/2–tiggy: 144°
	Ided–5–pip: 126°
	Toe–4–pip: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{10}}}\right)\approx 103.28253^{\circ }$
	Ided–6–toe: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Tiggy–6–toe: $\arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.76124^{\circ }$
Related polytopes
Army	Semi-uniform Prix
Regiment	Pirgaghi
Conjugate	Small prismatohecatonicosihecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	–1080
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great prismatohecatonicosihecatonicosihexacosichoron, or giphihix, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 600 truncated octahedra, 120 truncated great icosahedra, and 120 icosidodecadodecahedra. 1 pentagonal prism, 1 truncated great icosahedron, 1 icosidodecadodecahedron, and 2 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" (#377).

• Klitzing, Richard. "giphihix".