# Great grand stellated hecatonicosachoron

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Great grand stellated hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Gogishi |

Coxeter diagram | x5/2o3o3o () |

Schläfli symbol | {5/2,3,3} |

Elements | |

Cells | 120 great stellated dodecahedra |

Faces | 720 pentagrams |

Edges | 1200 |

Vertices | 600 |

Vertex figure | Tetrahedron, edge length (√5–1)/2 |

Edge figure | gissid 5/2 gissid 5/2 gissid 5/2 |

Measures (edge length 1) | |

Circumradius | |

Edge radius | |

Face radius | |

Inradius | |

Hypervolume | |

Dichoral angle | 72° |

Central density | 191 |

Number of pieces | 9600 |

Level of complexity | 30 |

Related polytopes | |

Army | Hi |

Regiment | Gogishi |

Dual | Grand hexacosichoron |

Conjugate | 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 grand stellated hecatonicosachoron**, or **gogishi**, also commonly called the **great grand stellated 120-cell**, is one of the 10 regular Schläfli–Hess polychora. It has 120 great stellated dodecahedra as cells, joining 3 to an edge and 4 to a vertex.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a great grand stellated hecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

together with all the even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 1: Regular Polychora" (#16).

- Bowers, Jonathan. "How to Make Gogishi".

- Klitzing, Richard. "gogishi".

- Wikipedia Contributors. "Great grand stellated 120-cell".