# Joined hexacosichoron

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Joined hexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Tibbic |

Coxeter diagram | o5m3o3o () |

Elements | |

Cells | 1200 triangular tegums |

Faces | 3600 isosceles triangles |

Edges | 720+2400 |

Vertices | 120+600 |

Vertex figure | 600 tetrahedra, 120 rhombic triacontahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Rectified hecatonicosachoron |

Abstract & topological properties | |

Flag count | 43200 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | Yes |

Nature | Tame |

The **joined hexacosichoron**, also known as the **triangular-tegmatic chiliadiacosichoron** or **tibbic**, is a convex isochoric polychoron with 1200 triangular tegums as cells. It can be obtained as the dual of the rectified hecatonicosachoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are times the length of those of the hecatonicosachoron.

The ratio between the longest and shortest edges is 1: ≈ 1:1.63131. Each face is an isosceles triangle that uses one long and two short edges.

## Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

- Triangular tegum (1200): Rectified hecatonicosachoron
- Isosceles triangle (3600): Semi-uniform small rhombated hecatonicosachoron
- Edge (720): Rectified hexacosichoron
- Edge (2400): Semi-uniform small disprismatohexacosihecatonicosachoron
- Vertex (120): Hexacosichoron
- Vertex (600): Hecatonicosachoron

## External links[edit | edit source]

- Klitzing, Richard. "tibbic".