# Rhombipyramidal hecatonenneacontadichoron

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Rhombipyramidal hecatonenneacontadichoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | m4m3o3m () |

Elements | |

Cells | 192 rhombic pyramids |

Faces | 192+192 scalene triangles, 96 rhombi |

Edges | 48+64+64+96+96 |

Vertices | 8+16+24+32 |

Vertex figure | 32 triangular bipyramids, 24 octagonal bipyramids, 8 triakis octahedra, 16 rhombic dodecahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Prismatorhombated hexadecachoron |

Abstract & topological properties | |

Flag count | 6144 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | Yes |

Nature | Tame |

The **rhombipyramidal hecatonenneacontadichoron** is a convex isochoric polychoron with 192 skew rhombic pyramids as cells. It can be obtained as the dual of the prismatorhombated hexadecachoron.

It can also be constructed as the convex hull of a tesseract, a hexadecachoron, an icositetrachoron (as a rectified hexadecachoron), and a rectified tesseract. If the tesseract has edge length 1, the hexadecachoron has edge length , the icositetrachoron has edge length , and the rectified tesseract has edge length .