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.
Originalsprache | englisch |
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Titel | Proc. 34th European Workshop on Computational Geometry EuroCG '18 |
Erscheinungsort | Berlin, Germany |
Seiten | 31:1-31:6 |
Publikationsstatus | Veröffentlicht - 2018 |
Veranstaltung | 34th European Workshop on Computational Geometry: EuroCG 2018 - FU Berlin, Berlin, Deutschland Dauer: 21 März 2018 → 23 März 2018 https://conference.imp.fu-berlin.de/eurocg18/home |
Konferenz
Konferenz | 34th European Workshop on Computational Geometry |
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Kurztitel | EuroCG 2018 |
Land/Gebiet | Deutschland |
Ort | Berlin |
Zeitraum | 21/03/18 → 23/03/18 |
Internetadresse |