# Tri-icositetradiminished hexacosichoron

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Tri-icositetradiminished hexacosichoron | |
---|---|

Rank | 4 |

Type | Noble |

Space | Spherical |

Notation | |

Bowers style acronym | Tridex |

Elements | |

Cells | 72 bi-tridiminished icosahedra |

Faces | 144 isosceles triangles, 72 isosceles trapezoids |

Edges | 48+72+72 |

Vertices | 48 |

Vertex figure | Tri-tridiminished icosahedron |

Measures (as derived from unit hexacosichoron) | |

Edge lengths | Short edges (72): 1 |

Long edges (48+72): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Tridex |

Regiment | Tridex |

Dual | Bi-icositetradiminished hexacosichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (B_{3}/2)●G_{2}, order 144 |

Convex | Yes |

Nature | Tame |

The **tri-icositetradiminished hexacosichoron** or **tridex**, also known as the **tetragonal-antiwedge heptacontadichoron** or **tetragonal-antiwedge hexafold pyritocubiswirlchoron**, is a noble polychoron with 72 bi-tridiminished icosahedra as cells. 9 cells join at each vertex. It can be obtained by diminishing the vertices of three icositetrachora from the hexacosichoron, and is the dual of the bi-icositetradiminished hexacosichoron.

The ratio between the longest and shortest edges is 1: ≈ 1:1.61803.

## External links[edit | edit source]

- Wikipedia Contributors. "Tri-24-diminished 600-cell".
- Klitzing, Richard. "tridex".