# Order-4 hexagonal tiling

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Order-4 hexagonal tiling | |
---|---|

Rank | 3 |

Type | Regular |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Shexat |

Coxeter diagram | x6o4o () |

Schläfli symbol | {6,4} |

Elements | |

Faces | 2N hexagons |

Edges | 6N |

Vertices | 3N |

Vertex figure | Square, edge length √3 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Shexat |

Regiment | Shexat |

Dual | Order-6 square tiling |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [6,4] |

Convex | Yes |

The **order-4 hexagonal tiling** is a regular tiling of the hyperbolic plane. 4 hexagons join at each vertex.

It can be formed by rectifying the order-6 hexagonal tiling.

## Representations[edit | edit source]

The order-4 hexagonal tiling has the following Coxeter diagrams:

- x6o4o (full symmetry)
- o6x6o () (as rectified order-6 hexagonal tiling)
- x3x6o6*a (hexagons of 3 types, trapezivert)

## Related polytopes[edit | edit source]

Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|

Order-4 hexagonal tiling | shexat | {6,4} | x6o4o | |

Truncated order-4 hexagonal tiling | toshexat | t{6,4} | x6x4o | |

Tetrahexagonal tiling | tehat | r{6,4} | o6x4o | |

Truncated order-6 square tiling | thisquat | t{4,6} | o6x4x | |

Order-6 square tiling | hisquat | {4,6} | o6o4x | |

Small rhombitetrahexagonal tiling | srotehat | rr{6,4} | x6o4x | |

Great rhombitetrahexagonal tiling | grotehat | tr{6,4} | x6x4x | |

Snub tetrahexagonal tiling | snatehat | sr{6,4} | s6s4s |

## External links[edit | edit source]

- Klitzing, Richard. "Shexat".

- Wikipedia Contributors. "Order-4 hexagonal tiling".