# Heptagonal tiling

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Heptagonal tiling | |
---|---|

Rank | 3 |

Type | Regular |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Heat |

Coxeter diagram | x7o3o () |

Schläfli symbol | {7,3} |

Elements | |

Faces | 6N Heptagons |

Edges | 21N |

Vertices | 14N |

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

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Heat |

Regiment | Heat |

Dual | Order-7 triangular tiling |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [7,3] |

Convex | Yes |

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

This tiling is the simplest tiling with three regular polygons at each vertex that neither fits in Euclidean space like the hexagonal tiling does, nor folds into spherical space like the dodecahedron (pentagons), cube (squares), or tetrahedron (triangles).

## Related polytopes[edit | edit source]

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

Heptagonal tiling | heat | {7,3} | x7o3o | |

Truncated heptagonal tiling | theat | t{7,3} | x7x3o | |

Triheptagonal tiling | thet | r{7,3} | o7x3o | |

Truncated order-7 triangular tiling | thetrat | t{3,7} | o7x3x | |

Order-7 triangular tiling | hetrat | {3,7} | o7o3x | |

Small rhombitriheptagonal tiling | srothet | rr{7,3} | x7o3x | |

Great rhombitriheptagonal tiling | grothet | tr{7,3} | x7x3x | |

Snub triheptagonal tiling | snathet | sr{7,3} | s7s3s |

## External links[edit | edit source]

- Wikipedia Contributors. "Heptagonal tiling".
- Nan Ma. "Heptagonal tiling {7,3}".