# Sphenoidal pentacosiheptacontahexachoron

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Sphenoidal pentacosiheptacontahexachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m3m4m3o () |

Elements | |

Cells | 576 sphenoids |

Faces | 288+288 isosceles triangles, 576 scalene triangles |

Edges | 96+144+192+288 |

Vertices | 24+24+96 |

Vertex figure | 96 triangular bipyramids, 24 triakis octahedra, 24 disdyakis dodecahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Great rhombated icositetrachoron |

Abstract & topological properties | |

Flag count | 13824 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | Yes |

Nature | Tame |

The **sphenoidal pentacosiheptacontahexachoron** is a convex isochoric polychoron with 576 sphenoids as cells. It can be obtained as the dual of the great rhombated icositetrachoron.

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