# Hexagonal tiling prism

Jump to navigation
Jump to search

Hexagonal tiling prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Coxeter diagram | x6o3o2x () |

Elements | |

Cells | ∞ hexagonal prisms, 2 hexagonal tilings |

Faces | ∞ hexagons, ∞ squares |

Edges | ∞+∞ |

Vertices | ∞ |

Vertex figure | Triangular pyramid |

Related polytopes | |

Army | Hexagonal tiling prism |

Regiment | Hexagonal tiling prism |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}×A_{1} |

Convex | Yes |

Nature | Tame |

The **hexagonal tiling prism** is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 hexagonal tilings and ∞ hexagonal prisms. Each vertex joins 1 square tiling and 3 hexagonal prisms. It is a prism based on the hexagonal tiling.

## Vertex coordinates[edit | edit source]

A hexagonal tiling prism of edge length 1 has vertex coordinates given by, where range over the integers:

- ,
- .

## Representations[edit | edit source]

A hexagonal tiling prism has the following Coxeter diagrams:

- x2x6o3o () (full symmetry)
- x2o6x3x () (as truncated triangular tiling prism)
- x2x3x3x3*b () (P
_{3}×A_{1}symmetry, as omnitruncated cyclotriangular tiling prism) - x2s6x3x () (additional alternated faceting form)

## External links[edit | edit source]

- Wikipedia contributors. "Convex uniform honeycomb#Frieze forms".