# Great hecatonicosachoron

Great hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Gohi |

Coxeter diagram | x5o5/2o5o () |

Schläfli symbol | {5,5/2,5} |

Elements | |

Cells | 120 great dodecahedra |

Faces | 720 pentagons |

Edges | 720 |

Vertices | 120 |

Vertex figure | Small stellated dodecahedron, edge length (1+√5)/2 |

Edge figure | gad 5 gad 5 gad 5 gad 5 gad 5 |

Measures (edge length 1) | |

Circumradius | |

Edge radius | |

Face radius | |

Inradius | |

Hypervolume | |

Dichoral angle | 144° |

Central density | 6 |

Number of pieces | 3600 |

Level of complexity | 6 |

Related polytopes | |

Army | Ex |

Regiment | Ex |

Company | Gohi |

Dual | Great hecatonicosachoron |

Conjugate | Grand stellated hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

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

It is a faceting of the hexacosichoron, sharing its vertices and edges. The great dodecahedral cells are in the vertex-figure planes of the hexacosichoron.

It is one of two regular star polychora to be self-dual, the other one being the grand stellated hecatonicosachoron, which is the conjugate of this polychoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the hexacosichoron.

## Related polychora[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 1: Regular Polychora" (#8).

- Klitzing, Richard. "gohi".

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

- Wikipedia Contributors. "Great 120-cell".