# Ditrigonary triangular-hemiapeirogonal tiling

The **ditrigonary triangular-hemiapeirogonal tiling**, or **ditatha**, is a nonconvex uniform tiling of the Euclidean plane. 3 triangles and 3 apeirogons join at each vertex of this tiling.

Ditrigonary triangular-hemiapeirogonal tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Ditatha |

Coxeter diagram | x3/2o3o∞*a () |

Elements | |

Faces | MN triangles, 3N apeirogons |

Edges | 3MN |

Vertices | MN |

Vertex figure | Hemitripod |

Related polytopes | |

Army | Trat |

Regiment | Trat |

Conjugate | None |

Abstract & topological properties | |

Flag count | 12MN |

Orientable | Yes |

Genus | ∞ |

Properties | |

Symmetry | P_{3} |

Convex | No |

Nature | Tame |

It is based on the same edge set as the triangular tiling, while only using half its triangles, such that no edge joins two triangles.

## External links edit

- Klitzing, Richard. "ditatha".
- McNeill, Jim. "Infinite and Semi".