标题： 非平坦正方形的铺砌：一种表征 显示英文标题

标题： Tilings with nonflat squares: a characterization

摘要： 受二维材料系统建模的启发，我们研究了三维中相同非平面正方形的排列。 我们证明了这种排列的精细几何结构完全由正方形相互取向的模式来表征，并且这些模式是周期性的且一维的。 与平面情况不同，瓷砖的非平面性产生了非平凡的几何结构，其中配置可以在一个方向上弯曲、起皱甚至卷曲。 显示英文摘要

摘要： 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.