# Truncated hexagonal tiling

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Truncated hexagonal tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Toxat |

Coxeter diagram | x6x3o () |

Elements | |

Faces | 2N triangles, N dodecagons |

Edges | 3N+6N |

Vertices | 6N |

Vertex figure | Isosceles triangle, edge lengths 1, (√2+√6)/2, (√2+√6)/2 |

Measures (edge length 1) | |

Vertex density | |

Related polytopes | |

Army | Toxat |

Regiment | Toxat |

Dual | Triakis triangular tiling |

Conjugate | Quasitruncated hexagonal tiling |

Abstract & topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | V_{3} |

Convex | Yes |

The **truncated hexagonal tiling**, or **toxat**, is one of the eleven convex uniform tilings of the Euclidean plane. 1 triangle and 2 dodecagons join at each vertex of this tiling. As its name suggests, it is the truncation of the regular hexagonal tiling.

## Related tilings[edit | edit source]

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

Hexagonal tiling | hexat | {6,3} | x6o3o | |

Truncated hexagonal tiling | toxat | t{6,3} | x6x3o | |

Trihexagonal tiling | that | r{6,3} | o6x3o | |

Truncated triangular tiling = Hexagonal tiling | hexat | t{3,6} | o6x3x | |

Triangular tiling | trat | {3,6} | o6o3x | |

Small rhombitrihexagonal tiling | srothat | rr{6,3} | x6o3x | |

Great rhombitrihexagonal tiling | grothat | tr{6,3} | x6x3x | |

Snub trihexagonal tiling | snathat | sr{6,3} | s6s3s |

## External links[edit | edit source]

- Klitzing, Richard. "toxat".

- Wikipedia Contributors. "Truncated hexagonal tiling".