A Note on Planar Monohedral Tilings

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem Konferenzband

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.
Originalspracheenglisch
TitelProc. 34th European Workshop on Computational Geometry EuroCG '18
ErscheinungsortBerlin, Germany
Seiten31:1-31:6
PublikationsstatusVeröffentlicht - 2018
Veranstaltung34th European Workshop on Computational Geometry - FU Berlin, Berlin, Deutschland
Dauer: 21 Mär 201823 Mär 2018
https://conference.imp.fu-berlin.de/eurocg18/home

Konferenz

Konferenz34th European Workshop on Computational Geometry
KurztitelEuroCG 2018
LandDeutschland
OrtBerlin
Zeitraum21/03/1823/03/18
Internetadresse

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