### Abstract

Original language | English |
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Title of host publication | Proc. 34th European Workshop on Computational Geometry EuroCG '18 |

Place of Publication | Berlin, Germany |

Pages | 31:1-31:6 |

Publication status | Published - 2018 |

Event | 34th European Workshop on Computational Geometry - FU Berlin, Berlin, Germany Duration: 21 Mar 2018 → 23 Mar 2018 https://conference.imp.fu-berlin.de/eurocg18/home |

### Conference

Conference | 34th European Workshop on Computational Geometry |
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Abbreviated title | EuroCG 2018 |

Country | Germany |

City | Berlin |

Period | 21/03/18 → 23/03/18 |

Internet address |

### Cite this

*Proc. 34th European Workshop on Computational Geometry EuroCG '18*(pp. 31:1-31:6). Berlin, Germany.

**A Note on Planar Monohedral Tilings.** / Aichholzer, Oswin; Kerber, Michael; Talata, István; Vogtenhuber, Birgit.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*Proc. 34th European Workshop on Computational Geometry EuroCG '18.*Berlin, Germany, pp. 31:1-31:6, 34th European Workshop on Computational Geometry, Berlin, Germany, 21/03/18.

}

TY - GEN

T1 - A Note on Planar Monohedral Tilings

AU - Aichholzer, Oswin

AU - Kerber, Michael

AU - Talata, István

AU - Vogtenhuber, Birgit

PY - 2018

Y1 - 2018

N2 - A planar monohedral tiling is a decomposition of $R^2$ into congruent tiles. We say that such a tiling has the flag property if for each triple of tiles that intersect pairwise, the three tiles intersect in a common point. We show that for convex tiles, there exist only three classes of tilings that are not flag, and they all consist of triangular tiles; in particular, each convex tiling using polygons with $ngeq 4$ vertices is flag. We also show that an analogous statement for the case of non-convex tiles is not true by presenting a family of counterexamples.

AB - A planar monohedral tiling is a decomposition of $R^2$ into congruent tiles. We say that such a tiling has the flag property if for each triple of tiles that intersect pairwise, the three tiles intersect in a common point. We show that for convex tiles, there exist only three classes of tilings that are not flag, and they all consist of triangular tiles; in particular, each convex tiling using polygons with $ngeq 4$ vertices is flag. We also show that an analogous statement for the case of non-convex tiles is not true by presenting a family of counterexamples.

M3 - Conference contribution

SP - 31:1-31:6

BT - Proc. 34th European Workshop on Computational Geometry EuroCG '18

CY - Berlin, Germany

ER -