Fig. 1: Overview of some typical kirigami/origami strategies.

a Schematic illustrations of folding, bending and twisting. b Mountain/valley fold orientations and patterns of fixed/free nodes in a Miura-ori pattern31. c Hyperboloid constructed by employing different densities of facets. d Generalized cylindrical Miura-ori patterns31. e Statistics of the scale and the type of stimulus employed in reported 3D microscale/nanoscale kirigami/origami techniques34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85. b–d Reprinted with permission from ref. 31