# Truncated square tiling

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Truncated square tiling | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Tosquat |

Coxeter diagram | x4x4o () |

Elements | |

Faces | N squares, N octagons |

Edges | 2N+4N |

Vertices | 4N |

Vertex figure | Isosceles triangle, edge lengths √2, √2+√2, √2+√2 |

Measures (edge length 1) | |

Vertex density | |

Related polytopes | |

Army | Tosquat |

Regiment | Tosquat |

Dual | Tetrakis square tiling |

Conjugate | Quasitruncated square tiling |

Abstract & topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | R_{3} |

Convex | Yes |

The **truncated square tiling**, or **tosquat**, is one of the eleven convex uniform tilings of the Euclidean plane. 1 square and 2 octagons join at each vertex of this tiling. As its name suggests, it is the truncation of the regular square tiling.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a truncated square tiling of edge length 1 are given by all permutations of

where *i* and *j* range over the integers.

## Representations[edit | edit source]

A truncated square tiling has the following Coxeter diagrams:

- x4x4o (regular)
- x4x4x (as omnitruncated square tiling)
- s4o4x (as alternated facting)
- s4x4x

## Related tilings[edit | edit source]

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

Square tiling | squat | {4,4} | x4o4o | |

Truncated square tiling | tosquat | t{4,4} | x4x4o | |

Rectified square tiling = Square tiling | squat | r{4,4} | o4x4o | |

Truncated square tiling | tosquat | t{4,4} | o4x4x | |

Square tiling | squat | {4,4} | o4o4x | |

Cantellated square tiling = Square tiling | squat | rr{4,4} | x4o4x | |

Omnitruncated square tiling = Truncated square tiling | tosquat | tr{4,4} | x4x4x | |

Snub square tiling | snasquat | sr{4,4} | s4s4s |

## External links[edit | edit source]

- Klitzing, Richard. "tosquat".

- Wikipedia Contributors. "Truncated square tiling".