# Elongated triangular tiling

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Elongated triangular tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Etrat |

Elements | |

Faces | 2N triangles, N squares |

Edges | N+2N+2N |

Vertices | 2N |

Vertex figure | Irregular Pentagon, edge lengths 1, 1, 1, √2, √2 |

Related polytopes | |

Army | Etrat |

Regiment | Etrat |

Dual | Prismatic pentagonal tiling |

Conjugate | Retroelongated triangular tiling |

Abstract & topological properties | |

Flag count | 20N |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | W_{2}❘W_{2}+ |

Convex | Yes |

Nature | Tame |

The **elongated triangular tiling**, or **etrat**, is one of the eleven convex uniform tilings of the Euclidean plane. 3 triangles and 2 squares join at each vertex of this tiling.

It is the only one of the 11 regular and uniform convex tilings of the plane to not be derivable from the regulars by truncation operations or alternation. It can be thought of as being constructed from the triangular tiling with layers of squares being inserted between adjacent layers of triangles. It can also be considered a blend of infinitely many apeirogonal antiprisms and apeirogonal prisms.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of an elongated triangular tiling of edge length 1 are given by

where i and j range over the integers.

## External links[edit | edit source]

- Klitzing, Richard. "etrat".
- Wikipedia contributors. "Elongated triangular tiling".
- McNeill, Jim. The 'traditional' eleven tessellations.
- Complex Uniform Tessellations on the Euclid Plane.