Learning the rules of kirigami

All good origami artists should have in their repertoire certain basic folds—the petal, the reverse, the mountain, to name just a few. Skillfully deployed, those basic folds can serve as building blocks for intricate, original creations. Now Randall Kamien and coworkers at the University of Pennsylvania have used concepts from condensed-matter theory to identify basic elements in a related art form: kirigami, the art of cutting, folding, and pasting. The researchers specifically consider kirigami on a graphene-like honeycomb lattice, under constraints designed to mimic bond networks in real two-dimensional materials. Cuts that remove part of a lattice are allowed, for instance, but only if subsequent folding and bond reformation around the excised area can restore the lattice's continuity. Also, the folded structures must preserve the original bond lengths. Applying topological arguments, the researchers identify two fundamental cuts from which all other allowable cuts derive. Each of the fundamental cuts prescribes a specific 3D fold; by mixing and matching them, one can create kirigami templates that fold into bow-tie structures (illustrated here with a paper model), boxes, staircases, and other 3D shapes. Like its better-known cousin, kirigami could prove useful for designing self-assembling nanostructures. But because in kirigami unwanted material is snipped away at the outset, the authors note, it should in principle allow more complicated structures to be achieved with fewer, simpler folds. (T. Castle et al., Phys. Rev. Lett., in press.)