### Abstract

We consider a tiling of a square by finitely many tiles each of which is a rectangle. We do not assume that the tiles are mutually congruent. Such a tiling is called irreducible if for any two tiles the union of them is not a rectangle. A tiling is called generic if no four tiles meet in a point. A tilling is trivial if it has only one tile. A tile r in a generic tiling of a square is called a spiral if it is contained in the interior of the square and for each edge e of r there is a tile s adjacent to r such that the straight line containing e intersects the interior of s. We show that a nontrivial generic irreducible tiling of a square has a spiral.

Original language | English |
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Pages (from-to) | 175-184 |

Number of pages | 10 |

Journal | Journal of Geometry |

Volume | 90 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2008 Dec 1 |

### Keywords

- Spiral
- Tiling

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Motohashi, T., & Taniyama, K. (2008). An irreducible rectangle tiling contains a spiral.

*Journal of Geometry*,*90*(1-2), 175-184. https://doi.org/10.1007/s00022-008-1923-5