Grand stellated hecatonicosachoron

Grand stellated hecatonicosachoron
(OFF file)
Rank	4
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Gashi
Coxeter diagram	x5/2o5o5/2o ()
Schläfli symbol	{5/2,5,5/2}
Elements
Cells	120 small stellated dodecahedra
Faces	720 pentagrams
Edges	720
Vertices	120
Vertex figure	Great dodecahedron, edge length (√5–1)/2
Edge figure	sissid 5/2 sissid 5/2 sissid 5/2 sissid 5/2 sissid 5/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt5-1}{2} \approx 0.61803$
Edge radius	$\frac{\sqrt{5-2\sqrt5}}{2} \approx 0.36327$
Face radius	$\sqrt{\frac{5-2\sqrt5}{5}} \approx 0.32492$
Inradius	$\frac{3-\sqrt5}{4} \approx 0.19098$
Hypervolume	$15\frac{7\sqrt5-15}{4} \approx 2.44678$
Dichoral angle	72°
Central density	66
Number of pieces	7200
Level of complexity	16
Related polytopes
Army	Ex
Regiment	Gishi
Company	Gishi
Dual	Grand stellated hecatonicosachoron
Conjugate	Great hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The grand stellated hecatonicosachoron, or gashi, also commonly called the grand stellated 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 small stellated dodecahedra as cells, joining 5 to an edge and 12 to a vertex in the form of a great dodecahedron.

It is a faceting of the great stellated hecatonicosachoron, sharing its vertices, edges, and faces.

It is one of two regular star polychora to be self-dual, the other one being the great hecatonicosachoron, which is the conjugate of this polychoron.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 1: Regular Polychora" (#13).

• Klitzing, Richard. "gashi".

• Nan Ma. "Grand stellated 120-cell {5/2, 5, 5/2}".

• Wikipedia Contributors. "Grand stellated 120-cell".