# Octagonal tiling

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Octagonal tiling | |
---|---|

Rank | 3 |

Type | Regular |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Ocat |

Coxeter diagram | x8o3o () |

Schläfli symbol | {8,3} |

Elements | |

Faces | 3N octagons |

Edges | 12N |

Vertices | 8N |

Vertex figure | Triangle, edge length √2+√2 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Ocat |

Regiment | Ocat |

Dual | Order-8 triangular tiling |

Abstract & topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [8,3] |

Convex | Yes |

The **order-3 octagonal tiling**, or just **octagonal tiling**, is a regular tiling of the hyperbolic plane. 3 octagons join at each vertex.

It can be formed by truncating the order-8 square tiling.

## Representations[edit | edit source]

The octagonal tiling has the following Coxeter diagrams:

- x8o3o (main symmetry)
- o8x4x (as truncated order-8 square tiling)
- x4x4x4*a (octagons of three types)

## 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. "Ocat".

- Wikipedia Contributors. "Octagonal tiling".