A Note on Planar Monohedral Tilings

Research output: Chapter in Book/Report/Conference proceedingConference paper


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
Publication statusPublished - 2018
Event34th European Workshop on Computational Geometry: EuroCG 2018 - FU Berlin, Berlin, Germany
Duration: 21 Mar 201823 Mar 2018


Conference34th European Workshop on Computational Geometry
Abbreviated titleEuroCG 2018
Internet address

Cite this