Great retrosphenoverted hecatonicosidishecatonicosachoron

Great retrosphenoverted hecatonicosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Grawv hidy
Coxeter diagram	o5/2x3x5/3o5*b ()
Elements
Cells	120 dodecadodecahedra, 120 truncated great icosahedra, 120 icosidodecadodecahedra
Faces	1440 pentagons, 720+1440 pentagrams, 2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Crossed wedge, edge lengths (√5–1)/2 (two edges of base rectangle and top edge), (1+√5)/2 (other 2 base edges), and √3 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {7-2{\sqrt {5}}}}\approx 1.58993$
Hypervolume	$15{\frac {905-333{\sqrt {5}}}{4}}\approx 601.46011$
Dichoral angles	Ided–5–did: 108°
	Did–5/2–tiggy: 108°
	Ided–5/2–ided: 72°
	Ided–6–tiggy: 60°
Related polytopes
Army	Srahi
Regiment	Sirgashi
Conjugate	Small retrosphenoverted hecatonicosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	–1560
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great retrosphenoverted hecatonicosidishecatonicosachoron, or grawv hidy, is a nonconvex uniform polychoron that consists of 120 dodecadodecahedra, 120 truncated great icosahedra, and 120 icosidodecadodecahedra. 1 dodecadodecahedron, 2 truncated great icosahedra, and 2 icosidodecadodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small rhombated grand stellated hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#208).

• Klitzing, Richard. "grawv hidy".