Mathematical Physics
[Submitted on 4 Aug 2021
]
Title: Tilings with nonflat squares: a characterization
Title: 非平坦正方形的铺砌：一种表征
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.
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