Great prismatohecatonicosidishecatonicosachoron

Great prismatohecatonicosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Giphidy
Coxeter diagram	x5/3x3x5/3o5*b ()
Elements
Cells	720 pentagrammic prisms, 120 quasitruncated small stellated dodecahedra, 120 icosidodecadodecahedra, 120 great quasitruncated icosidodecahedra
Faces	3600 squares, 1440 pentagons, 1440 pentagrams, 2400 hexagons, 1440 decagrams
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, √(5–√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {13-5{\sqrt {5}}}}\approx 1.34895$
Hypervolume	$15{\frac {1637{\sqrt {5}}-3635}{4}}\approx 95.41230$
Dichoral angles	Ided–6–gaquatid: 120°
	Quit sissid–10/3–gaquatid: 108°
	Ided–5–quit sissid: 72°
	Ided–5/2–stip: 54°
	Gaquatid–4–stip: $\arccos \left({\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 31.71747^{\circ }$
Related polytopes
Army	Semi-uniform Prahi
Regiment	Quippirgashi
Conjugate	Small prismatohecatonicosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	–1560
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great prismatohecatonicosidishecatonicosachoron, or giphidy, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 quasitruncated small stellated dodecahedra, 120 icosidodecadodecahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagrammic prism, 1 quasitruncated small stellated dodecahedron, 1 icosidodecadodecahedron, 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 stellated hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#386).

• Klitzing, Richard. "giphidy".