# Great heptagonal tiling

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Great heptagonal tiling | |
---|---|

Rank | 3 |

Type | Regular |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Gheat |

Coxeter diagram | o7/2o7x () |

Schläfli symbol | {7, 7/2} |

Elements | |

Faces | 2N heptagons |

Edges | 7N |

Vertices | 2N |

Vertex figure | Heptagram, edge length 2cos(π/7) |

Measures (edge length 1) | |

Circumradius | |

Central density | 3 |

Related polytopes | |

Army | Hetrat |

Regiment | Hetrat |

Dual | Stellated heptagonal tiling |

Convex core | Heptagonal tiling |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | [7,3] |

Convex | No |

The **great heptagonal tiling** or **gheat**, also known as the **heptagrammic-order heptagonal tiling**, is a regular star tiling of the hyperbolic plane. 7 heptagons join at each vertex in a heptagrammic arrangement.

It is a faceting of the order-7 triangular tiling, using the bases of its heptagonal pyramid caps as faces. It is related to the spherical great dodecahedron, which can be obtained from a similar faceting of the regular icosahedron.

## External links[edit | edit source]

- Klitzing, Richard. "x7o7/2o".

- Wikipedia Contributors. "Heptagrammic-order heptagonal tiling".
- Nan Ma. "Heptagrammic-order heptagonal tiling {7,7/2}".