# Square-antitegmatic hecatontetracontatetrachoron

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Square-antitegmatic hecatontetracontatetrachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | m3o4o3m |

Elements | |

Cells | 144 square antitegums |

Faces | 576 kites |

Edges | 288+384 |

Vertices | 48+192 |

Vertex figure | 192 triangular bipyramids, 48 cubes |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Small prismatotetracontoctachoron |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | F4×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **square-antitegmatic hecatontetracontatetrachoron** is a convex isochoric polychoron with 144 square antitegums as cells. It can be obtained as the dual of the small prismatotetracontoctachoron.

It can also be constructed as the convex hull of 2 dual icositetrachora and 2 opposite rectified icositetrachora. If the icositetrachora have edge length 1, the rectified icositetrachora have edge length .

## Isogonal derivatives[edit | edit source]

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

- Square antitegum (144): Small prismatotetracontoctachoron
- Kite (576): Rectified small prismatotetracontoctachoron
- Edge (288): Tetracontoctachoron
- Edge (384): Bitruncatotetracontoctachoron
- Vertex (48): Bitetracontoctachoron
- Vertex (192): Biambotetracontoctachoron