Great hecatonicosintercepted hecatonicosachoron

Great hecatonicosintercepted hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gohiny
Elements
Cells	120 great icosidodecahedra, 120 quasitruncated great stellated dodecahedra
Faces	2400 triangles, 720 pentagrams, 720 decagrams
Edges	3600
Vertices	1200
Vertex figure	Triangular toroprism, edge lengths 1 (base edges), (√5-1)/2 (side edges of rectangles), and √(5-√5)/2 (side edges of triangles)
Edge figure	gid 5/2 gid 3 quitgissid 10/3 quitgissid 10/3 quitgissid 3
Measures (edge length 1)
Circumradius	$\frac{3\sqrt3-\sqrt{15}}{2} ≈ 0.66158$
Hypervolume	$\frac{1881\sqrt5-4195}{4} ≈ 13.80483$
Dichoral angles	Gid–5/2–gid: 72°
	Gid–3–quit gissid: 60°
	Quit gissid–10/3–quit gissid: 36°
Number of pieces	85200
Level of complexity	201
Related polytopes
Army	Rahi
Regiment	Rigogishi
Conjugate	Small hecatonicosintercepted hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract properties
Euler characteristic	1200
Topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The great hecatonicosintercepted hecatonicosachoron, or gohiny, is a nonconvex uniform polychoron that consists of 120 great icosidodecahedra and 120 quasitruncated great stellated dodecahedra. 3 great icosidodecahedra and 6 quasitruncated great stellated dodecahedra join at each vertex.

It is wild because it has great icosidodecahedra intercepted by decagrams.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 3: Triangular Rectates" (#59).

• Klitzing, Richard. "gohiny".