# Order-4 apeirogonal tiling

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Order-4 apeirogonal tiling | |
---|---|

Rank | 3 |

Type | Regular, paracompact |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Squazat |

Coxeter diagram | x∞o4o () |

Schläfli symbol | {∞,4} |

Elements | |

Faces | 4N apeirogons |

Edges | 2NM |

Vertices | NM |

Vertex figure | Square, edge length 2 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Squazat |

Regiment | Squazat |

Dual | Order-∞ square tiling |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [∞,4] |

Convex | Yes |

The **order-4 apeirogonal tiling** is a paracompact regular tiling of the hyperbolic plane. 4 apeirogons join at each vertex.

It can be formed by rectifying the order-∞ apeirogonal tiling.

## Representations[edit | edit source]

The order-4 apeirogonal tiling has the following Coxeter diagrams:

- x∞o4o (full symmetry)
- o∞x∞o () (as rectified order-∞ apeirogonal tiling)
- x∞x∞o∞*a (three types of faces) ()

## Related polytopes[edit | edit source]

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

Order-4 apeirogonal tiling | squazat | {∞,4} | ||

Truncated order-4 apeirogonal tiling | tosquazat | t{∞,4} | ||

Tetraapeirogonal tiling | tezt | r{∞,4} | ||

Truncated order-∞ square tiling | tazsquat | t{4,∞} | ||

Order-∞ square tiling | azsquat | {4,∞} | ||

Small rhombitetraapeirogonal tiling | srotezt | rr{∞,4} | ||

Great rhombitetraapeirogonal tiling | grotezt | tr{∞,4} | ||

Snub tetraapeirogonal tiling | sr{∞,4} |

## External links[edit | edit source]

- Klitzing, Richard. "squazat".

- Wikipedia Contributors. "Order-4 apeirogonal tiling".