# Tetrakis hexacosichoron

The **tetrakis hexacosichoron**, also known as the **triangular-pyramidal dischilliatetracosichoron**, is a convex isochoric polychoron with 2400 triangular pyramids as cells. It can be obtained as the dual of the truncated hecatonicosachoron.

Tetrakis hexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m5m3o3o () |

Elements | |

Cells | 2400 triangular pyramids |

Faces | 1200 triangles, 3600 isosceles triangles |

Edges | 720+2400 |

Vertices | 120+600 |

Vertex figure | 600 tetrahedra, 120 triakis icosahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Truncated hecatonicosachoron |

Abstract & topological properties | |

Flag count | 57600 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | Yes |

Nature | Tame |

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are times the length of those of the hecatonicosachoron. Varying the hexacosichoron's edge length to be anything more than times that of the hecatonicosachoron gives a fully symmetric variant of this polychoron.