# Order-∞ pentagonal tiling

Jump to navigation
Jump to search

Order-∞ pentagonal tiling | |
---|---|

Rank | 3 |

Type | Regular, paracompact |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Azpat |

Coxeter diagram | o∞o5x () |

Schläfli symbol | {5,∞} |

Elements | |

Faces | 2NM pentagons |

Edges | 5NM |

Vertices | 10N |

Vertex figure | Apeirogon, edge length (1+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Azpat |

Regiment | Azpat |

Dual | Order-5 apeirogonal tiling |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [∞,5] |

Convex | Yes |

The **order-∞ pentagonal tiling** or **infinite-order pentagonal tiling** is a paracompact regular tiling of the hyperbolic plane. Infinitely many ideal pentagons join at each vertex. All vertices are ideal points at infinity.

## Representations[edit | edit source]

An order–∞ pentagonal tiling has the following Coxeter diagrams:

- o∞o5x (full symmetry)
- o5x5o∞*a (pentagons of two types)

## Related polytopes[edit | edit source]

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

Order-5 apeirogonal tiling | pazat | {∞,5} | ||

Truncated order-5 apeirogonal tiling | topazat | t{∞,5} | ||

Pentaapeirogonal tiling | pazt | r{∞,5} | ||

Truncated order-∞ pentagonal tiling | tazpat | t{5,∞} | ||

Order-∞ pentagonal tiling | azpat | {5,∞} | ||

Small rhombipentaapeirogonal tiling | sropazt | rr{∞,5} | ||

Great rhombipentaapeirogonal tiling | gropazt | tr{∞,5} | ||

Snub pentaapeirogonal tiling | sr{∞,5} |

## External links[edit | edit source]

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