# Grand hexacosichoron

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Grand hexacosichoron | |
---|---|

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 | |

Edge radius | |

Face radius | |

Inradius | |

Hypervolume | |

Dichoral angle | |

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 | H_{4}, 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[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- 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".