Tilings with Nonflat Squares: A Characterization

Friedrich M, Seitz M, Stefanelli U (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Milan Journal of Mathematics Springer Verlag (Germany)

DOI: 10.1007/s00032-022-00350-5

Abstract

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.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Friedrich, M., Seitz, M., & Stefanelli, U. (2022). Tilings with Nonflat Squares: A Characterization. Milan Journal of Mathematics. https://doi.org/10.1007/s00032-022-00350-5

MLA:

Friedrich, Manuel, Manuel Seitz, and Ulisse Stefanelli. "Tilings with Nonflat Squares: A Characterization." Milan Journal of Mathematics (2022).

BibTeX: Download