Origami Lattices and Folding-induced Lattice Transformations

Lattices and their underlying symmetries play a central role in determining the physical properties and applications of many natural and engineered materials. By bridging the lattice geometry and rigid-folding kinematics, this study elucidates that origami offers a comprehensive solution to a long-standing challenge regarding the lattice-based materials: how to systematically construct a lattice and transform it among different symmetric configurations in a predictable, scalable, and reversible way? Based on a group of origamis consisting of generic degree-4 vertices, we successfully construct all types of 2D and 3D Bravais lattices, and demonstrate that they can undergo all diffusionless phase transformations via rigid-folding (i.e., dilation, extension, contraction, shear, and shuffle). Such folding-induced lattice transformations can trigger fundamental lattice-symmetry switches, which can either maintain or reconstruct the nearest neighborhood relationships according to a continuous symmetry measure. This study can foster the next generation of transformable lattice structures and materials with on-demand property tuning capabilities.