Hexagon tilings of the plane that are not edge-to-edge

Frettlöh D, Glazyrin A, Langi Z (2021)
Acta Mathematica Hungarica volume 164(2): 341-349.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Frettlöh, DirkUniBi; Glazyrin, A.; Langi, Z.
Abstract / Bemerkung
An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer k >= 3, there exists a normal tiling of the Euclidean plane by convex hexagons of unit area with exactly k irregular vertices. Using the same approach we show that there are normal edge-to-edge tilings of the plane by hexagons of unit area and exactly k many n-gons (n > 6) of unit area. A result of Akopyan yields an upper bound for k depending on the maximal diameter and minimum area of the tiles. Our result complements this with a lower bound for the extremal case, thus showing that Akopyan's bound is asymptotically tight.
Stichworte
tiling; normal tiling; monotypic tiling; irregular vertex
Erscheinungsjahr
2021
Zeitschriftentitel
Acta Mathematica Hungarica volume
Band
164
Ausgabe
2
Seite(n)
341-349
ISSN
0236-5294
eISSN
1588-2632
Page URI
https://pub.uni-bielefeld.de/record/2956022

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Frettlöh D, Glazyrin A, Langi Z. Hexagon tilings of the plane that are not edge-to-edge. Acta Mathematica Hungarica volume. 2021;164(2):341-349.
Frettlöh, D., Glazyrin, A., & Langi, Z. (2021). Hexagon tilings of the plane that are not edge-to-edge. Acta Mathematica Hungarica volume, 164(2), 341-349. https://doi.org/10.1007/s10474-021-01155-5
Frettlöh, D., Glazyrin, A., and Langi, Z. (2021). Hexagon tilings of the plane that are not edge-to-edge. Acta Mathematica Hungarica volume 164, 341-349.
Frettlöh, D., Glazyrin, A., & Langi, Z., 2021. Hexagon tilings of the plane that are not edge-to-edge. Acta Mathematica Hungarica volume, 164(2), p 341-349.
D. Frettlöh, A. Glazyrin, and Z. Langi, “Hexagon tilings of the plane that are not edge-to-edge”, Acta Mathematica Hungarica volume, vol. 164, 2021, pp. 341-349.
Frettlöh, D., Glazyrin, A., Langi, Z.: Hexagon tilings of the plane that are not edge-to-edge. Acta Mathematica Hungarica volume. 164, 341-349 (2021).
Frettlöh, Dirk, Glazyrin, A., and Langi, Z. “Hexagon tilings of the plane that are not edge-to-edge”. Acta Mathematica Hungarica volume 164.2 (2021): 341-349.

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