Great hecatonicosachoron

Great hecatonicosachoron
(OFF file)
Rank	4
Type	Regular
Notation
Bowers style acronym	Gohi
Coxeter diagram	x5o5/2o5o ()
Schläfli symbol	{5,5/2,5}
Elements
Cells	120 great dodecahedra
Faces	720 pentagons
Edges	720
Vertices	120
Vertex figure	Small stellated dodecahedron, edge length (1+√5)/2
Edge figure	gad 5 gad 5 gad 5 gad 5 gad 5
Measures (edge length 1)
Circumradius	${\frac {1+{\sqrt {5}}}{2}}\approx 1.61803$
Edge radius	${\frac {\sqrt {5+2{\sqrt {5}}}}{2}}\approx 1.53884$
Face radius	${\sqrt {\frac {5+2{\sqrt {5}}}{5}}}\approx 1.37638$
Inradius	${\frac {3+{\sqrt {5}}}{4}}\approx 1.30902$
Hypervolume	$15{\frac {15+7{\sqrt {5}}}{4}}\approx 114.94678$
Dichoral angle	144°
Central density	6
Number of external pieces	3600
Level of complexity	6
Related polytopes
Army	Ex
Regiment	Ex
Company	Gohi
Dual	Great hecatonicosachoron
Conjugate	Grand stellated hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	14400
Euler characteristic	0
Schläfli type	{5,5,5}
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	1
Convex	No
Nature	Tame

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

It is a faceting of the hexacosichoron, sharing its vertices and edges. The great dodecahedral cells are in the vertex-figure planes of the hexacosichoron.

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

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the hexacosichoron.

Related polychora

The great hecatonicosachoron is the captain of a company in the regiment of the hexacosichoron, having the same faces as the grand hecatonicosachoron.

Uniform polychoron compounds composed of great hecatonicosachora include:

• Great diacositetracontachoron (2)
• Great chirohexacosichoron (5)
• Great chirododecahedral hyperprismatochoron (6)
• Great dishexacosichoron (10)
• Great disdodecahedral hyperprismatochoron (12)

External links

• Bowers, Jonathan. "Category 1: Regular Polychora" (#8).

• Klitzing, Richard. "gohi".
• Nan Ma. "Great 120-cell {5, 5/2, 5}".

• Wikipedia contributors. "Great 120-cell".