# Great rhombitrioctagonal tiling

Jump to navigation
Jump to search

Great rhombitrioctagonal tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Grotoct |

Coxeter diagram | x8x3x () |

Elements | |

Faces | 12N squares, 8N hexagons, 3N hexadecagons |

Edges | 24N+24N+n24N |

Vertices | 48N |

Vertex figure | Scalene triangle, edge lengths √2, √2+√2, √2+√2+√2 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Grotoct |

Regiment | Grotoct |

Dual | 3-8 kisrhombille tiling |

Abstract & topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [8,3] |

Convex | Yes |

The **great rhombitrioctagonal tiling** or **grotoct**, also called the **truncated trioctagonal tiling**, is a uniform tiling of the hyperbolic plane. 1 square, 1 hexagon and 1 hexadecagon join at each vertex. It can be formed by cantitruncation of either the octagonal tiling or its dual order-8 triangular tiling, or equivalently by truncation of the trioctagonal tiling.

## 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. "grotoct".

- Wikipedia Contributors. "Truncated trioctagonal tiling".