# Grand hexacosichoron

Grand hexacosichoron Rank4
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGax
Coxeter diagramo5/2o3o3x (         )
Schläfli symbol{3,3,5/2}
Elements
Cells600 tetrahedra
Faces1200 triangles
Edges720
Vertices120
Vertex figureGreat icosahedron, edge length 1
Edge figuretet 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 density191
Number of pieces36000
Level of complexity118
Related polytopes
ArmyEx
RegimentGishi
CompanyGofix
DualGreat grand stellated hecatonicosachoron
ConjugateHexacosichoron
Convex coreHexacosichoron
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

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.

## Vertex coordinates

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