# Truncated order-8 triangular tiling

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Truncated order-8 triangular tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Totrat |

Coxeter diagram | o8x3x () |

Elements | |

Faces | 8N hexagons, 3N octagons |

Edges | 12N+24N |

Vertices | 24N |

Vertex figure | Isosceles triangle, edge lengths √2+√2, √3, √3 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Totrat |

Regiment | Totrat |

Dual | Octakis octagonal tiling |

Abstract & topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [8,3] |

Convex | Yes |

The **truncated order-8 triangular tiling** or **totrat** is a uniform tiling of the hyperbolic plane. 2 hexagons and 1 octagon join at each vertex. It can be formed from the truncation of the order-8 triangular tiling.

It is also the omnitruncate of the (4,3,3) family of tilings, with Coxeter diagram .

## Representations[edit | edit source]

A truncated order-8 triangular tiling has the following Coxeter diagrams:

- o8x3x (full symmetry)
- x3x3x4*a (half symmetry)

## Related polytopes[edit | edit source]

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

Octagonal tiling | ocat | {8,3} | x8o3o | |

Truncated octagonal tiling | tocat | t{8,3} | x8x3o | |

Trioctagonal tiling | toct | r{8,3} | o8x3o | |

Truncated order-8 triangular tiling | totrat | t{3,8} | o8x3x | |

Order-8 triangular tiling | otrat | {3,8} | o8o3x | |

Small rhombitrioctagonal tiling | srotoct | rr{8,3} | x8o3x | |

Great rhombitrioctagonal tiling | grotoct | tr{8,3} | x8x3x | |

Snub trioctagonal tiling | snatoct | sr{8,3} | s8s3s |

## External links[edit | edit source]

- Klitzing, Richard. "x3x8o".

- Wikipedia Contributors. "Truncated order-8 triangular tiling".