Great faceted hexacosichoron

Great faceted hexacosichoron
(OFF file)
Rank	4
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Gofix
Coxeter diagram	o5o5/2o3x ()
Schläfli symbol	{3,5/2,5}
Elements
Cells	120 great icosahedra
Faces	1200 triangles
Edges	720
Vertices	120
Vertex figure	Small stellated dodecahedron, edge length 1
Edge figure	gike 3 gike 3 gike 3 gike 3 gike 3
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	$\frac{3\sqrt3-\sqrt{15}}{6} \approx 0.22053$
Inradius	$\frac{3-\sqrt5}{4} \approx 0.19098$
Hypervolume	$25\frac{7-3\sqrt5}{4} \approx 1.82373$
Dichoral angle	120°
Central density	76
Number of external pieces	7200
Level of complexity	12
Related polytopes
Army	Ex, edge length $\frac{3-\sqrt5}{2}$
Regiment	Gishi
Company	Gofix
Dual	Great grand hecatonicosachoron
Conjugate	Faceted hexacosichoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	14400
Euler characteristic	480
Schläfli type	{3,5,5}
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

The great faceted hexacosichoron is a faceting of the great stellated hecatonicosachoron, sharing its vertices and edges. The cells are in the same planes as the small stellated dodecahedra of the grand stellated hecatonicosachoron.

Cross-sections

Vertex coordinates

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

Related polychora

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

Uniform polychoron compounds composed of faceted hexacosichora include:

• Great faceted chirotetrahedral dishexacosichoron (2)
• Great faceted snub pentishecatonicosachoron (5)
• Great chiricosahedral hyperprismatochoron (6)
• Great faceted snub decahecatonicosachoron (10)
• Great disicosahedral hyperprismatochoron (12)

External links

• Bowers, Jonathan. "Category 1: Regular Polychora" (#14).

• Klitzing, Richard. "gofix".

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

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