Great hecatonicosiprismatodishecatonicosachoron

Great hecatonicosiprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ghipady
Coxeter diagram	x5x3x5o3/2*b ()
Elements
Cells	720 pentagonal prisms, 120 truncated dodecahedra, 120 great icosicosidodecahedra, 120 great rhombicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagons, 2400 hexagons, 1440 decagons
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths 1, √3, (1+√5)/2, √3; lateral edge lengths √2, √2, √(5+√5)/2, √(5+√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {10+3{\sqrt {5}}}}\approx 4.08757$
Hypervolume	$5{\frac {6025+3249{\sqrt {5}}}{4}}\approx 16612.4811$
Dichoral angles	Giid–5–pip: 162°
	Grid–4–pip: $\arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }$
	Giid–3–tid: 120°
	Tid–10–grid: 72°
	Giid–6–grid: 60°
Related polytopes
Army	Semi-uniform Prix, edge lengths ${\frac {3-{\sqrt {5}}}{2}}$ (truncated dodecahedra), ${\frac {{\sqrt {5}}-1}{2}}$ (bases of triangular prisms)
Regiment	Gid thipady
Conjugate	Small hecatonicosiprismatodishecatonicosachoron
Abstract & topological properties
Flag count	230400
Euler characteristic	–600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great hecatonicosiprismatodishecatonicosachoron, or ghipady, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated dodecahedra, 120 great icosicosidodecahedra, and 120 great rhombicosidodecahedra. 1 pentagonal prism, 1 truncated dodecahedron 1 great icosicosidodecahedron, and 2 great rhombicosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#428).

• Klitzing, Richard. "ghipady".