Great grand hecatonicosachoron

Great grand hecatonicosachoron
(OFF file)
Rank	4
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Gaghi
Coxeter diagram	x5o5/2o3o ()
Schläfli symbol	{5,5/2,3}
Elements
Cells	120 great dodecahedra
Faces	720 pentagons
Edges	1200
Vertices	120
Vertex figure	Great stellated dodecahedron, edge length (1+√5)/2
Edge figure	gad 5 gad 5 gad 5
Measures (edge length 1)
Circumradius	1
Edge radius	$\frac{\sqrt3}{2} \approx 0.86603$
Face radius	$\sqrt{\frac{5-\sqrt5}{10}} \approx 0.52573$
Inradius	$\frac{\sqrt5-1}{4} \approx 0.30902$
Hypervolume	$15\frac{5+\sqrt5}{4} \approx 27.13525$
Dichoral angle	72°
Central density	76
Number of external pieces	10800
Level of complexity	33
Related polytopes
Army	Ex, edge length $\frac{\sqrt5-1}{2}$
Regiment	Sishi
Dual	Great faceted hexacosichoron
Conjugate	Small stellated hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	14400
Euler characteristic	–480
Schläfli type	{5,5,3}
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great grand hecatonicosachoron, or gaghi, also commonly called the great grand 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great dodecahedra as cells, joining 3 to an edge and 12 to a vertex in the form of a great stellated dodecahedron.

It is a faceting of the small stellated hecatonicosachoron, sharing its vertices and edges. It is the only other regular polychoron to do so.

Cross-sections

Vertex coordinates

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

Related polychora

Uniform polychoron compounds composed of great grand hecatonicosachora include:

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

External links

• Bowers, Jonathan. "Category 1: Regular Polychora" (#11).

• Bowers, Jonathan. "How to Make Gaghi".

• Klitzing, Richard. "gaghi".

• Nan Ma. "Great grand 120-cell {5, 5/2, 3}".

• Wikipedia Contributors. "Great grand 120-cell".