  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.
