# Prismatotruncated hexadecachoric tetracomb

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Prismatotruncated hexadecachoric tetracomb | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Pataht |

Coxeter diagram | o3x4o3x3x () |

Elements | |

Tera | 32N triangular-hexagonal duoprisms, 12N cuboctahedral prisms, 3N prismatorhombated tesseracts, N small rhombated icositetrachora |

Cells | 96N+96N triangular prisms, 72N cubes, 96N hexagonal prisms, 24N truncated tetrahedra, 24N cuboctahedra, 24N small rhombicuboctahedra |

Faces | 96N+192N triangles, 144N+288N+288N squares, 96N hexagons |

Edges | 144N+288N+576N |

Vertices | 288N |

Vertex figure | Wedge pyramid, edge lengths 1 (two base edges and top edge of wedge), √2 (sides and remaining base edges of wedge and lacings to base rectangle), and √3 (lacings to top edge) |

Related polytopes | |

Army | Pataht |

Regiment | Pataht |

Conjugate | Quasiprismatotruncated hexadecachoric tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | U_{5} |

Convex | Yes |

Nature | Tame |

The **prismatotruncated hexadecachoric tetracomb** or **pataht**, also called the **runcitruncated hexadecachoric tetracomb** is a convex uniform tetracomb. 1 small rhombated icositetrachoron, 2 prismatorhombated tesseracts, 1 cuboctahedral prism, and 2 triangular-hexagonal duoprisms join at each vertex of this tessellation. As the name suggests, it is the runcitruncation of the hexadecachoric tetracomb.

## External links[edit | edit source]

- Klitzing, Richard. "pataht".
- Wikipedia contributors. "Runcitruncated 16-cell honeycomb".