# Tetrakis hexadecachoron

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Tetrakis hexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | m4m3o3o () |

Elements | |

Cells | 64 triangular pyramids |

Faces | 32 triangles, 96 isosceles triangles |

Edges | 24+64 |

Vertices | 8+16 |

Vertex figure | 16 tetrahedra, 8 triakis octahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Truncated tesseract |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | Yes |

Nature | Tame |

The **tetrakis hexadecachoron**, also known as the **triangular-pyramidal hexacontatetrachoron**, is a convex isochoric polychoron with 64 triangular pyramids as cells. It can be obtained as the dual of the truncated tesseract.

As the tetrakis square duotegum, it is the square member of an infinite family of isochoric tetrakis duotegums.

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