# Small sphenoidal heptachiliadiacosichoron

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Small sphenoidal heptachiliadiacosichoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | o5m3m3m () |

Elements | |

Cells | 7200 sphenoids |

Faces | 3600+3600 isosceles triangles, 7200 scalene triangles |

Edges | 1200+1440+2400+3600 |

Vertices | 120+600+720 |

Vertex figure | 720 pentagonal bipyramids, 600 tetrakis hexahedra, 120 pentakis dodecahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Great rhombated hexacosichoron |

Abstract & topological properties | |

Flag count | 172800 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | Yes |

Nature | Tame |

The **small sphenoidal heptachiliadiacosichoron** is a convex isochoric polychoron with 7200 sphenoids as cells. It can be obtained as the dual of the great rhombated hexacosichoron.

It can also be constructed as the convex hull of a hecatonicosachoron, a hexacosichoron, and a rectified hexacosichoron. If the hecatonicosachoron has edge length 1, the hexacosichoron has edge length and the rectified hexacosichoron has edge length .