Spider-morphs: Designing 3D shapes from multiple tapered <i>elasticæ</i>.

Foldable three-dimensional (3D) structures are important in a wide range of engineering applications. Transforming flat two-dimensional sheets with cuts into 3D structures, or kirigami, has emerged as an exciting manufacturing paradigm. However, achieving a particular 3D shape usually requires multiple materials and/or the application of external stimuli. Here we introduce a design framework for forming approximately axisymmetric 3D structures by harnessing the buckling of multiple tapered elastic sheets (the legs) connected in a central portion (the body). Together this creates a spider-like structure that morphs in 3D: a spider-morph. We design spider-morphs that deform into axisymmetric 3D structures with positive, negative, and variable Gaussian curvature. We conduct both numerical simulations and physical experiments to verify our theoretical approach.