# Truncated great faceted hexacosichoron

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

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tigfix |

Coxeter diagram | o5o5/2x3x () |

Elements | |

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

Faces | 1440 pentagrams, 1200 hexagons |

Edges | 720+3600 |

Vertices | 1440 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tiggy–6–tiggy: 120° |

Sissid–5/2–tiggy: 108° | |

Central density | 76 |

Number of external pieces | 15960 |

Level of complexity | 48 |

Related polytopes | |

Army | Semi-uniform Tex |

Regiment | Tigfix |

Conjugate | Truncated faceted hexacosichoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –480 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

## Cross-sectionsEdit

## Vertex coordinatesEdit

The vertices of a truncated great faceted hexacosichoron of edge length 1 are given by all even permutations of:

## Related polychoraEdit

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

## External linksEdit

- Bowers, Jonathan. "Category 2: Truncates" (#28).

- Klitzing, Richard. "tigfix".