Grand hecatonicosachoron

Grand hecatonicosachoron
(OFF file)
Rank	4
Type	Regular
Notation
Bowers style acronym	Gahi
Coxeter diagram	o5/2o3o5x ()
Schläfli symbol	{5,3,5/2} $\{5,3,5\mid 3\}$
Elements
Cells	120 dodecahedra
Faces	720 pentagons
Edges	720
Vertices	120
Vertex figure	Great icosahedron, edge length (1+√5)/2
Edge figure	doe 5 doe 5 doe 5 doe 5 doe 5
Deep holes	1200 triangles
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	${\frac {1+{\sqrt {5}}}{4}}\approx 0.80902$
Hypervolume	$15{\frac {25+11{\sqrt {5}}}{4}}\approx 185.98780$
Dichoral angle	72°
Central density	20
Number of external pieces	21600
Level of complexity	44
Related polytopes
Army	Ex
Regiment	Ex
Company	Gohi
Dual	Great stellated hecatonicosachoron
Conjugate	Great stellated hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	14400
Euler characteristic	0
Schläfli type	{5,3,5}
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The grand hecatonicosachoron, or gahi, also commonly called the grand 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 dodecahedra as cells, joining 5 to an edge and 20 to a vertex in the form of a great icosahedron.

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

Cross-sections

Vertex coordinates

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

Related polychora

Uniform polychoron compounds composed of grand hecatonicosachora include:

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

External links

• Bowers, Jonathan. "Category 1: Regular Polychora" (#9).

• Klitzing, Richard. "gahi".
• Nan Ma. "Grand 120-cell {5, 3, 5/2}".

• Wikipedia contributors. "Grand 120-cell".

Bibliography

• McMullen, Peter (1998). "The groups of regular star polytopes" (PDF). Canadian Journal of Mathematics. 50: 426–448. doi:10.4153/CJM-1998-023-7.