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دراسة الشكل والزوايا في التكوين Figure.pptx

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PNAS Nexus, Volume 3, Issue 9, September 2024, pgae311, https://doi.org/10.1093/pnasnexus/pgae311 The content of this slide may be subject to copyright: please see the slide notes for details. Fig. 2. Soft tilings in the plane. We show soft monohedric tilings which are combinatorially equivalent to monohedral ...

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دراسة الشكل والزوايا في التكوين Figure.pptx

  • 1.
    PNAS Nexus, Volume3, Issue 9, September 2024, pgae311, https://doi.org/10.1093/pnasnexus/pgae311 The content of this slide may be subject to copyright: please see the slide notes for details. Fig. 2. Soft tilings in the plane. We show soft monohedric tilings which are combinatorially equivalent to monohedral ...

Editor's Notes

  • #1 Fig. 2. Soft tilings in the plane. We show soft monohedric tilings which are combinatorially equivalent to monohedral tilings with regular polygons. Each row shows combinatorially equivalent soft tilings, corresponding to regular triangulation (first row), the rectangular grid (second row), and the hexagonal honeycomb (third row). If, beyond combinatorial equivalence classes, we also distinguish between sharp and soft corners then we arrive at the 12 tilings shown in the figure. In each tiling one soft cell is highlighted by solid filling. We remark that the last two rows show soft tilings which are combinatorially equivalent to Dirichlet–Voronoi mosaics on point lattices (16). Unless provided in the caption above, the following copyright applies to the content of this slide: © The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.