# Truncated faceted hexacosichoron

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Truncated faceted hexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tiffix |

Coxeter diagram | o5/2o5x3x () |

Elements | |

Cells | 120 great dodecahedra, 120 truncated icosahedra |

Faces | 1440 pentagons, 1200 hexagons |

Edges | 720+3600 |

Vertices | 1440 |

Vertex figure | Pentagrammic pyramid, edge lengths (1+√5)/2 (base) and √3 (side) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gad–5–ti: 144° |

Ti–6–ti: 120° | |

Central density | 4 |

Number of external pieces | 2520 |

Level of complexity | 13 |

Related polytopes | |

Army | Tex |

Regiment | Tex |

Conjugate | Truncated great faceted hexacosichoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –480 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

## Cross-sections[edit | edit source]

## External links[edit | edit source]

- Bowers, Jonathan. "Category 2: Truncates" (#24).

- Klitzing, Richard. "tiffix".