Grand hexacosichoron

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Grand hexacosichoron
Rank4
TypeRegular
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
Edge radius
Face radius
Inradius
Hypervolume
Dichoral angle
Central density191
Number of external pieces36000
Level of complexity118
Related polytopes
ArmyEx, edge length
RegimentGishi
CompanyGofix
DualGreat grand stellated hecatonicosachoron
ConjugateHexacosichoron
Convex coreHexacosichoron
Abstract & topological properties
Flag count14400
Euler characteristic0
Schläfli type{3,3,5}
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.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

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

Related polychora[edit | edit source]

Uniform polychoron compounds composed of grand hexacosichora include:

External links[edit | edit source]