# Triangular prismatic honeycomb

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Triangular prismatic honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Tiph |

Coxeter diagram | xØo2x3o6o () |

Elements | |

Cells | 2N triangular prisms |

Faces | 2N triangles, 3N squares |

Edges | N+3N |

Vertices | N |

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

Related polytopes | |

Army | Tiph |

Regiment | Tiph |

Dual | Hexagonal prismatic honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2} |

Convex | Yes |

Nature | Tame |

The **triangular prismatic honeycomb**, or **tiph**, is a convex noble uniform honeycomb. 12 triangular prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the triangular tiling and the apeirogon.

## Vertex coordinates[edit | edit source]

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

- ,

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

## Representations[edit | edit source]

A triangular prismatic honeycomb has the following Coxeter diagrams:

- xØo2x3o6o ()
- xØx2x3o6o ()
- xØo2x3o3o3*c ()
- xØx2x3o3o3*c ()
- xØo2s3s3s3*c ()
- xØx2s3s3s3*c ()

## External links[edit | edit source]

- Klitzing, Richard. "tiph".
- Wikipedia contributors. "Triangular prismatic honeycomb".