Shape and topology morphing of closed surfaces integrating origami and kirigami.

A closed surface is generally more resistant to deformation and shape changes than an open surface. An empty closed box, for example, is stiffer and more stable than when it is open. The presence of an opening makes it less constrained, more deformable, and easier to morph, as demonstrated by several studies on open-surface morphing across patterns, materials, and scales. Here, we present a platform to morph closed surfaces with bistability that harnesses a balanced integration of origami and kirigami principles. By harmonizing panel rotation around creases nearly tangent to the closed surface and panel rotation around hinges nearly perpendicular to the closed surface, we show that origami-kirigami assemblages can shape-morph between a cube and a sphere, scale between spheres of dissimilar size, and change topology between a sphere and a torus, with programmed bistability. The framework offers a promising strategy for designing bistable reconfigurable structures and metamaterials with enclosed configurations.