Great retrotrishecatonicosachoron

Great retrotrishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Girthi
Elements
Cells	120 truncated great dodecahedra, 120 truncated great icosahedra, 120 icosidodecatruncated icosidodecahedra
Faces	1440 pentagrams, 2400 hexagons, 1440 decagons, 720 decagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Isosceles triangular retroprism, edge lengths (√5–1)/2 (2), √3 (4), √(5+√5)/2 (4), and √(5–√5)/2 (2)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {11-{\sqrt {5}}}{2}}}\approx 2.09332$
Hypervolume	$15{\frac {199{\sqrt {5}}-180}{2}}\approx 1987.33146$
Dichoral angles	Idtid–10–tigid: 72°
	Idtid–6–tiggy: 60°
	Tiggy–5/2–tigid: 36°
	Idtid–10/3–idtid: 36°
Related polytopes
Army	Semi-uniform srix
Regiment	Swavathi
Conjugate	Small retrotrishecatonicosachoron
Abstract & topological properties
Euler characteristic	–1560
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great retrotrishecatonicosachoron, or girthi, is a nonconvex uniform polychoron that consists of 120 truncated great icosahedra, 120 truncated great dodecahedra, and 120 icosidodecatruncated icosidodecahedra. Two truncated great icosahedra, two truncated great dodecahedra, and four icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small sphenoverted trishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#273).