# Truncated hexagonal prismatic honeycomb

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Truncated hexagonal prismatic honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Thaph |

Coxeter diagram | x∞o x6x3o |

Elements | |

Cells | 2N triangular prisms, N dodecagonal prisms |

Faces | 2N triangles, 3N+6N squares, N dodecagons |

Edges | 3N+6N+6N |

Vertices | 6N |

Vertex figure | Notch, edge lengths 1, (√2+√6)/2, (√2+√6)/2 (equatorial) and √2 (remaining edges) |

Related polytopes | |

Army | Thaph |

Regiment | Thaph |

Dual | Triakis triangular prismatic honeycomb |

Conjugate | Quasitruncated hexagonal prismatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2} |

Convex | Yes |

The **truncated hexagonal prismatic honeycomb**, or **thaph**, is a convex uniform honeycomb. 2 triangular prisms and 4 dodecagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the truncated hexagonal tiling and the apeirogon.

## Representations[edit | edit source]

A truncated hexagonal prismatic honeycomb has the following Coxeter diagrams:

- x∞o x6x3o
- x∞x x6x3o

## External links[edit | edit source]

- Klitzing, Richard. "thaph".

- Wikipedia Contributors. "Truncated hexagonal prismatic honeycomb".