Geometry
On the number of non-hexagons in a planar tiling
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 412-414.

We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons.

Nous donnons une démonstration simple d'un résultat de T. Stehling [4], assurant que dans tout pavage normal du plan par des polygones convexes d'au moins six côtés, les pavés qui ne sont pas des hexagones sont en nombre fini.

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DOI: 10.1016/j.crma.2018.03.005
Akopyan, Arseniy 1

1 Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
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Akopyan, Arseniy. On the number of non-hexagons in a planar tiling. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 412-414. doi : 10.1016/j.crma.2018.03.005. http://www.numdam.org/articles/10.1016/j.crma.2018.03.005/

[1] Fejes Tóth, L. Lagerungen in der Ebene, auf der Kugel und im Raum, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol. LXV, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1953

[2] Markelov, S. A question to friends mathematicians (a partition of the plane into convex heptagons), June 20, 2014 https://gaz-v-pol.livejournal.com/140610.html (URL:)

[3] Niven, I. Convex polygons that cannot tile the plane, Amer. Math. Mon., Volume 85 (1978) no. 10, pp. 785-792

[4] Stehling, T. Über kombinatorische und graphentheoretische Eigenschaften normaler Pflasterungen, Universität Dortmund, Germany, 1989 ProQuest LLC, Ann Arbor, MI, USA, PhD Thesis (Dr.rer.nat)

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