# Deltopyramidal pentacosiheptacontahexachoron

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Deltopyramidal pentacosiheptacontahexachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m3m4o3m () |

Elements | |

Cells | 576 kite pyramids |

Faces | 576+576 scalene triangles, 288 kites |

Edges | 144+192+192+288+288 |

Vertices | 24+24+96+96 |

Vertex figure | 96 triangular bipyramids, 96 hexagonal bipyramids, 24 tetrakis hexahedra, 24 deltoidal icositetrahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Prismatorhombated icositetrachoron |

Abstract & topological properties | |

Flag count | 18432 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | Yes |

Nature | Tame |

The **deltopyramidal pentacosiheptacontahexachoron** is a convex isochoric polychoron with 576 kite pyramids as cells.

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