Great prismatohexacosihecatonicosihecatonicosachoron

Great prismatohexacosihecatonicosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gippixhihy
Coxeter diagram	x5/3x3x3/2o3*b ()
Elements
Cells	1200 triangular prisms, 600 octahemioctahedra, 120 quasitruncated great stellated dodecahedra, 120 great quasitruncated icosidodecahedra
Faces	2400+2400 triangles, 3600 squares, 2400 hexagons, 1440 decagrams
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Skewed Bowtie pyramid, base edge lengths 1, √3, 1, √3; lateral edge lengths √2, √2, √(5–√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {48-21{\sqrt {5}}}}\approx 1.02106$
Hypervolume	$25{\frac {6459-2879{\sqrt {5}}}{4}}\approx 133.50183$
Dichoral angles	Quit gissid–3–oho: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Oho–6–gaquatid: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Quit gissid–10/3–gaquatid: 72°
	Gaquatid–4–trip: $\arccos \left({\frac {{\sqrt {15}}-{\sqrt {3}}}{4}}\right)\approx 69.09484^{\circ }$
	Oho–3–trip: $\arccos \left({\frac {{\sqrt {30}}-{\sqrt {6}}}{8}}\right)\approx 67.76124^{\circ }$
Related polytopes
Army	Semi-uniform Prahi
Regiment	Quippirgax
Conjugate	Small prismatohexacosihecatonicosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great prismatohexacosihecatonicosihecatonicosachoron, or gippixhihy, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 600 octahemioctahedra, 120 quasitruncated great stellated dodecahedra, and 120 great quasitruncated icosidodecahedra. 1 triangular prism, 1 octahemioctahedron, 1 quasitruncated great stellated dodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the quasiprismatorhombated grand hexacosichoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#392).

• Klitzing, Richard. "gippixhihy".