# Trihexagonal prismatic honeycomb

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Trihexagonal prismatic honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Thiph |

Coxeter diagram | x∞o o6x3o |

Elements | |

Cells | 2N triangular prisms, N hexagonal prisms |

Faces | 2N triangles, 6N squares, N hexagons |

Edges | 3N+6N |

Vertices | 3N |

Vertex figure | Rectangular tegum, edge lengths 1 and √3 (equatorial) and √2 (sides) |

Related polytopes | |

Army | Thiph |

Regiment | Thiph |

Dual | Rhombic prismatic honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2} |

Convex | Yes |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

The vertices of a trihexagonal prismatic honeycomb of edge length 1 are given by:

Where i, j, and k range over the integers.

## Representations[edit | edit source]

A trihexagonal prismatic honeycomb has the following Coxeter diagrams:

- x∞o o6x3o
- x∞x o6x3o
- x∞o x3x3o3*a
- x∞x x3x3o3*a

## External links[edit | edit source]

- Klitzing, Richard. "thiph".
- Wikipedia contributors. "Trihexagonal prismatic honeycomb".