# Truncated grand hecatonicosachoron

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Truncated grand hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Taghi |

Coxeter diagram | o5/2o3x5x () |

Elements | |

Cells | 120 great icosahedra, 120 truncated dodecahedra |

Faces | 2400 triangles, 720 decagons |

Edges | 720+3600 |

Vertices | 1440 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gike–3–tid: 120° |

Tid–10–tid: 72° | |

Central density | 20 |

Number of external pieces | 21720 |

Level of complexity | 71 |

Related polytopes | |

Army | Semi-uniform Tex, edge lengths (icosahedra), 1 (surrounded by truncated tetrahedra) |

Regiment | Tighi |

Conjugate | Quasitruncated great stellated hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Flag count | 57600 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

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

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 2: Truncates" (#26).

- Klitzing, Richard. "taghi".