# Hexagonal prismatic honeycomb

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Hexagonal prismatic honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Hiph |

Coxeter diagram | xØo2x6o3o () |

Elements | |

Cells | N hexagonal prisms |

Faces | 3N squares, N hexagons |

Edges | 2N+3N |

Vertices | 2N |

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

Related polytopes | |

Army | Hiph |

Regiment | Hiph |

Dual | Triangular prismatic honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2} |

Convex | Yes |

Nature | Tame |

The **hexagonal prismatic honeycomb**, or **hiph**, is a convex noble uniform honeycomb. 6 hexagonal prisms join at each vertex of this honeycomb. It is the honeycomb product of the hexagonal tiling and the apeirogon.

This honeycomb can be alternated into a gyrated tetrahedral-octahedral honeycomb, which can be made uniform.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a hexagonal prismatic honeycomb of edge length 1 are given by:

- ,
- ,

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

## Representations[edit | edit source]

A hexagonal prismatic honeycomb has the following Coxeter diagrams:

- xØo2x6o3o ()
- xØx2x6o3o ()
- xØo2o6x3x ()
- xØx2o6x3x ()
- xØo2x3x3x3*c ()
- xØx2x3x3x3*c ()

## External links[edit | edit source]

- Klitzing, Richard. "hiph".
- Wikipedia contributors. "Hexagonal prismatic honeycomb".