Grand hexacosichoron

Grand hexacosichoron
(OFF file)
Rank	4
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Gax
Coxeter diagram	o5/2o3o3x ()
Schläfli symbol	{3,3,5/2}
Elements
Cells	600 tetrahedra
Faces	1200 triangles
Edges	720
Vertices	120
Vertex figure	Great icosahedron, edge length 1
Edge figure	tet 3 tet 3 tet 3 tet 3 tet 3
Measures (edge length 1)
Circumradius	$\frac{\sqrt5-1}{2} ≈ 0.61803$
Edge radius	$\frac{\sqrt{5-2\sqrt5}}{2} ≈ 0.36327$
Face radius	$\frac{3\sqrt3-\sqrt{15}}{6} ≈ 0.22053$
Inradius	$\frac{\sqrt{10}-2\sqrt2}{4} ≈ 0.083463$
Hypervolume	$25\frac{\sqrt5-2}{4} ≈ 1.47542$
Dichoral angle	$\arccos\left(\frac{3\sqrt5-1}{8}\right) ≈ 44.47751°$
Central density	191
Number of pieces	36000
Level of complexity	118
Related polytopes
Army	Ex
Regiment	Gishi
Company	Gofix
Dual	Great grand stellated hecatonicosachoron
Conjugate	Hexacosichoron
Convex core	Hexacosichoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The grand hexacosichoron, or gax, also commonly called the grand 600-cell, is one of the 10 regular Schläfli–Hess polychora. It has 600 regular tetrahedra 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 great stellated hecatonicosachoron, sharing its vertices and edges, and the faces of the great faceted hexacosichoron.

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" (#15).

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

• Klitzing, Richard. "gax".

• Nan Ma. "Grand 600-cell {3, 3, 5/2}".

• Wikipedia Contributors. "Grand 600-cell".