Prismatoquasirhombated great grand stellated hecatonicosachoron

Prismatoquasirhombated great grand stellated hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Paqrigagishi
Coxeter diagram	x5/3o3x3x ()
Elements
Cells	720 pentagrammic prisms, 1200 hexagonal prisms, 600 truncated tetrahedra, 120 quasirhombicosidodecahedra
Faces	2400 triangles, 3600+3600 squares, 1440 pentagrams, 2400 hexagons
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths 1, √2, (√5–1)/2, √2; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\frac {3{\sqrt {10}}-5{\sqrt {2}}}{2}}\approx 1.20788$
Hypervolume	$25{\frac {1814-779{\sqrt {5}}}{4}}\approx 450.64403$
Dichoral angles	Qrid–5/2–stip: 126°
	Qrid–3–tut: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Qrid–4–hip: $\arccos \left({\frac {{\sqrt {15}}-{\sqrt {3}}}{6}}\right)\approx 69.09484^{\circ }$
	Tut–6–hip: $\arccos \left({\frac {{\sqrt {30}}-{\sqrt {6}}}{8}}\right)\approx 67.76124^{\circ }$
	Stip–4–hip: $\arccos \left({\sqrt {\frac {10-2{\sqrt {5}}}{15}}}\right)\approx 52.62263^{\circ }$
Related polytopes
Army	Semi-uniform Prahi
Regiment	Gippixady
Conjugate	Prismatorhombated hecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The prismatoquasirhombated great grand stellated hecatonicosachoron, or paqrigagishi, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 1200 hexagonal prisms, 600 truncated tetrahedra, and 120 quasirhombicosidodecahedra. 1 pentagrammic prism, 2 hexagonal prisms, 1 truncated tetrahedron, and 1 quasirhombicosidodecahedron join at each vertex. It can be obtained by quasiruncitruncating the grand hexacosichoron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#407).

• Klitzing, Richard. "paqrigagishi".