A universal identity for the Poisson ratios of oblique Miura-ori

Certain origami and origami-like tessellations, such as the Miura-ori and the eggbox pattern, remarkably exhibit equal and opposite in-plane and out-of-plane Poisson ratios. In this talk, we propose and prove a generalization of this identity to all tessellations that can be obtained as the translation surface of one zigzag along another. These include in particular the entire family of oblique, i.e., non-orthotropic, Miura-ori. The proof is based on a perturbative scheme and makes some typical assumptions of rigid folding kinematics; it remains valid for small and large deformations whether the underlying tessellation is symmetrical, developable, flat-foldable, or not.