A Note on Planar Monohedral Tilings

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Abstract

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.
Original languageEnglish
Title of host publicationProc. 34th European Workshop on Computational Geometry EuroCG '18
Place of PublicationBerlin, Germany
Pages31:1-31:6
Publication statusPublished - 2018
Event34th European Workshop on Computational Geometry - FU Berlin, Berlin, Germany
Duration: 21 Mar 201823 Mar 2018
https://conference.imp.fu-berlin.de/eurocg18/home

Conference

Conference34th European Workshop on Computational Geometry
Abbreviated titleEuroCG 2018
CountryGermany
CityBerlin
Period21/03/1823/03/18
Internet address

Cite this

Aichholzer, O., Kerber, M., Talata, I., & Vogtenhuber, B. (2018). A Note on Planar Monohedral Tilings. In Proc. 34th European Workshop on Computational Geometry EuroCG '18 (pp. 31:1-31:6). Berlin, Germany.