Algorithmic design of origami mechanisms and tessellations

Abstract Origami, the ancient art of paper folding, embodies techniques for transforming a flat sheet into shapes arbitrary complexity. Although this makes origami conceptually attractive source inspiration when designing foldable structures and reconfigurable metamaterials multiple functionalities, their designs are still based on set well-studied patterns leaving full potential inaccessible design practitioners researchers. Here, we present generalized approach algorithmic rigidly-foldable exhibiting single kinematic degree freedom. We build conditions rigid foldability degree- n vertices to size The versatility is demonstrated by its capability not only generate, analyze optimize regular patterns, but also generate kirigami, generic three-dimensional panel-hinge assemblages tessellations. Due versatility, provides an inexhaustible inspire wide range applications.