# Small rhombitrihexagonal tiling

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Small rhombitrihexagonal tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Srothat |

Coxeter diagram | x6o3x () |

Elements | |

Faces | 2N triangles, 3N squares, N hexagons |

Edges | 6N+6n |

Vertices | 6N |

Vertex figure | Isosceles trapezoid, edge lengths 1, √2, √3, √2 |

Measures (edge length 1) | |

Vertex density | |

Related polytopes | |

Army | Srothat |

Regiment | Srothat |

Dual | Deltoidal trihexagonal tiling |

Conjugate | Quasirhombitrihexagonal tiling |

Abstract & topological properties | |

Flag count | 48N |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | V_{3} |

Convex | Yes |

Nature | Tame |

The **small rhombitrihexagonal tiling**, or **srothat**, also called simply the **rhombitrihexagonal tiling**, is one of the eleven convex uniform tilings of the Euclidean plane. 1 triangle, 1 hexagon, and 2 squares join at each vertex of this tiling. It can be formed by expanding the faces of either the triangular tiling or its dual hexagonal tiling outward..

## Representations[edit | edit source]

A small rhombitrihexagonal tiling has the following Coxeter diagrams:

- x6o3x () (full symmetry)
- x6s3s () (as edge-snub triangular tiling)

## Related tilings[edit | edit source]

The small rhombitrihexagonal tiling is the colonel of a three-member regiment that also includes the small hexatrihexagonal tiling and the small rhombihexagonal tiling.

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

Hexagonal tiling | hexat | {6,3} | x6o3o | |

Truncated hexagonal tiling | toxat | t{6,3} | x6x3o | |

Trihexagonal tiling | that | r{6,3} | o6x3o | |

Truncated triangular tiling = Hexagonal tiling | hexat | t{3,6} | o6x3x | |

Triangular tiling | trat | {3,6} | o6o3x | |

Small rhombitrihexagonal tiling | srothat | rr{6,3} | x6o3x | |

Great rhombitrihexagonal tiling | grothat | tr{6,3} | x6x3x | |

Snub trihexagonal tiling | snathat | sr{6,3} | s6s3s |

## External links[edit | edit source]

- Klitzing, Richard. "srothat".

- McNeill, Jim. "Star Tesselations Type 1".

- Wikipedia Contributors. "Rhombitrihexagonal tiling".