# Octakis icositetrachoron

Octakis icositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m3m4o3o () |

Elements | |

Cells | 192 triangular pyramids |

Faces | 96 triangles, 288 isosceles triangles |

Edges | 96+144 |

Vertices | 24+24 |

Vertex figure | 24 octahedra, 24 tetrakis hexahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Truncated icositetrachoron |

Abstract & topological properties | |

Flag count | 4608 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | Yes |

Nature | Tame |

The **octakis icositetrachoron**, also known as the **triangular-pyramidal hecatonicenneacontadichoron**, is a convex isochoric polychoron with 192 triangular pyramids as cells. It can be obtained as the dual of the truncated icositetrachoron.

It can also be obtained as the convex hull of two dually oriented icositetrachora, where one has edges exactly times the length of those of the other. Any convex hull of two dual icositetrachora where one is more than times the edge length of the other gives a fully symmetric variant of this polychoron.

## Variations[edit | edit source]

The octakis icositetrachoron has variants that remain isochoric under B_{4} symmetry (called the great sphenoidal hecatonenneacontadichoron) and D_{4} symmetry (called the tetrahedral hecatonenneacontadichoron).