Tilings with Nonflat Squares: A Characterization

Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and...

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Autores principales: Friedrich, Manuel, Seitz, Manuel, Stefanelli, Ulisse
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9242529/
https://www.ncbi.nlm.nih.gov/pubmed/35784394
http://dx.doi.org/10.1007/s00032-022-00350-5
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author Friedrich, Manuel
Seitz, Manuel
Stefanelli, Ulisse
author_facet Friedrich, Manuel
Seitz, Manuel
Stefanelli, Ulisse
author_sort Friedrich, Manuel
collection PubMed
description Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction.
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spelling pubmed-92425292022-06-30 Tilings with Nonflat Squares: A Characterization Friedrich, Manuel Seitz, Manuel Stefanelli, Ulisse Milan J Math Article Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction. Springer International Publishing 2022-03-24 2022 /pmc/articles/PMC9242529/ /pubmed/35784394 http://dx.doi.org/10.1007/s00032-022-00350-5 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Friedrich, Manuel
Seitz, Manuel
Stefanelli, Ulisse
Tilings with Nonflat Squares: A Characterization
title Tilings with Nonflat Squares: A Characterization
title_full Tilings with Nonflat Squares: A Characterization
title_fullStr Tilings with Nonflat Squares: A Characterization
title_full_unstemmed Tilings with Nonflat Squares: A Characterization
title_short Tilings with Nonflat Squares: A Characterization
title_sort tilings with nonflat squares: a characterization
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9242529/
https://www.ncbi.nlm.nih.gov/pubmed/35784394
http://dx.doi.org/10.1007/s00032-022-00350-5
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