# Truncated great hecatonicosachoron

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Truncated great hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tighi |

Coxeter diagram | x5x5/2o5o () |

Elements | |

Cells | 120 small stellated dodecahedra, 120 truncated great dodecahedra |

Faces | 1440 pentagrams, 720 decagons |

Edges | 720+3600 |

Vertices | 1440 |

Vertex figure | Pentagonal pyramid, edge lengths (√5–1)/2 (base) and √(5+√5)/2 (side) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sissid–5/2–tigid: 144° |

Tigid–10–tigid: 144° | |

Central density | 6 |

Number of external pieces | 3720 |

Level of complexity | 15 |

Related polytopes | |

Army | Semi-uniform Tex |

Regiment | Tighi |

Conjugate | Quasitruncated grand stellated hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –960 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **truncated great hecatonicosachoron**, or **tighi**, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 120 truncated great dodecahedra. One small stellated dodecahedron and five truncated great dodecahedra join at each vertex. As the name suggests, it can be obtained by truncating the great hecatonicosachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a truncated great hecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

## Related polychora[edit | edit source]

The truncated great hecatonicosachoron is the colonel of a two-member regiment that also includes the truncated grand hecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 2: Truncates" (#25).

- Klitzing, Richard. "tighi".