# Order-7 triangular tiling

Jump to navigation
Jump to search

Order-7 triangular tiling | |
---|---|

Rank | 3 |

Type | Regular |

Space | Hyperbolic |

Notation | |

Bowers style acronym | Hetrat |

Coxeter diagram | o7o3x () |

Schläfli symbol | {3,7} |

Elements | |

Faces | 14N Triangles |

Edges | 21N |

Vertices | 6N |

Vertex figure | Heptagon, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Hetrat |

Regiment | Hetrat |

Dual | Heptagonal tiling |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | [7,3] |

Convex | Yes |

The **order-7 triangular tiling** or **hetrat** is a regular tiling of the hyperbolic plane. 7 triangles join at each vertex.

It is the first tiling of triangles to be hyperbolic, rather than spherical or Euclidean.

## Related polytopes[edit | edit source]

This tiling shares its edges with the great heptagonal tiling.

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]

- Klitzing, Richard. "Hetrat".

- Nan Ma. "Order-7 triangular tiling {3,7}".

- Wikipedia Contributors. "Order-7 triangular tiling".