Great retrosphenoverted hecatonicosidishecatonicosachoron

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.

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

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".