Rigidly flat-foldable class of lockable origami-inspired metamaterials with topological stiff states.

Origami crease patterns have inspired the design of reconfigurable materials that can transform their shape and properties through folding. Unfortunately, most designs cannot provide load-bearing capacity, and those that can, do so in certain directions but collapse along the direction of deployment, limiting their use as structural materials. Here, we merge notions of kirigami and origami to introduce a rigidly foldable class of cellular metamaterials that can flat-fold and lock into several states that are stiff across multiple directions, including the deployment direction. Our metamaterials rigidly fold with one degree of freedom and can reconfigure into several flat-foldable and spatially-lockable folding paths due to face contact. Locking under compression yields topology and symmetry changes that impart multidirectional stiffness. Additionally, folding paths and mixed-mode configurations can be activated in situ to modulate their properties. Their load-bearing capacity, flat-foldability, and reprogrammability can be harnessed for deployable structures, reconfigurable robots, and low-volume packaging.