c Prototype of stacked square twist pattern during testing. b Simulation of the structure shown in a (the prototype corresponds only to a part (approx. a Prototype of stacked square twist pattern with its highlighted graph-based formalization. The operations are intercompatible and are used here to define the more complicated layer adding, extruding, and tessellation procedures, which are then applied to expediently generate various origami structures of considerable complexity.įig. To that end, we introduce four algorithmic operations, involving expansion, quadrilateral-closing, translating, mirroring, and gluing.

By using the generalized conditions for rigid foldability of degree-n vertices and graph-grammar based formalisms to describe an origami, we are able to computationally construct origami with quadrilateral facets, generic three-dimensional panel-hinge assemblages, and their tessellations (Fig. In our work, we present a computational approach for the design of origami mechanisms and tessellations of arbitrary size and complexity.

The ability to generate origami using advanced computational methods could drastically improve the applicability of origami for metamaterial design by increasing the range of viable solutions or to find alternative configurations beyond the handful of well-described origami patterns. The special property of origami to rigidly fold into almost any shape, renders the application to metamaterials a conceptually promising direction allowing for novel applications across many scientific and engineering domains.

An emerging direction to design mechanical metamaterials for new functionalities and complex behavior is in the application of origami.

Tessellation in nature