# Order-∞ apeirogonal tiling

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Order-∞ apeirogonal tiling | |
---|---|

Rank | 3 |

Type | Regular, paracompact |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Azazat |

Coxeter diagram | x∞o∞o () |

Schläfli symbol | {∞,∞} |

Elements | |

Faces | 2N apeirogons |

Edges | NM |

Vertices | 2N |

Vertex figure | Apeirogon, edge length 2 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Azazat |

Regiment | Azazat |

Dual | Order-∞ apeirogonal tiling |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [∞,∞] |

Convex | Yes |

The **order-∞ apeirogonal tiling** or **infinite-order apeirogonal tiling** is a paracompact regular tiling of the hyperbolic plane. Infinitely many apeirogons join at each vertex. It is self-dual.

## Representations[edit | edit source]

The order-∞ apeirogonal tiling has the following Coxeter diagrams:

- x∞o∞o (full symmetry)
- x∞o∞o∞*a (apeirogons of two types) ()

## Related polytopes[edit | edit source]

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

Order-∞ apeirogonal tiling | azazat | {∞,∞} | ||

Truncated order-∞ apeirogonal tiling = Apeirogonal tiling | azat | t{∞,∞} | ||

Apeiroapeirogonal tiling = Order-4 apeirogonal tiling | squazat | r{∞,∞} | ||

Truncated order-∞ apeirogonal tiling = Apeirogonal tiling | azat | t{∞,∞} | ||

Order-∞ apeirogonal tiling | azazat | {∞,∞} | ||

Small rhombiapeiroapeirogonal tiling = Tetraapeirogonal tiling | tezt | rr{∞,∞} | ||

Great rhombiapeiroapeirogonal tiling = Truncated order-4 apeirogonal tiling | tosquazat | tr{∞,∞} | ||

Snub apeiroapeirogonal tiling | sr{∞,∞} |

## External links[edit | edit source]

- Klitzing, Richard. "azazat".

- Wikipedia Contributors. "Infinite-order apeirogonal tiling".