Architecting three-dimensional reconfigurable matter from pop-up kirigami with programmable multistability

Mechanical pop-up systems, which reconfigure from two-dimensional (2D) into complex three-dimensional (3D) shapes, are promising for advanced manufacturing and deployable devices. Multistable pop-up kirigami systems are especially advantageous because their properties decouple the simple, 2D fabricated state from the complex, 3D operational state, which greatly simplifies manufacturing. We identify that these pop-up systems are designed by the multiloop coupling strategy, which, however, has traditionally been limited by the geometric symmetry. In this work, we extend this strategy by removing symmetry constraints to create a generalized pop-up kirigami platform that enables programmable multistability with controlled, asymmetric pop-up and twisting motions. Using this platform, we demonstrate previously inaccessible formations, including tristable units with two programmable spatial states and large-scale tessellations of interconnected units. We showcase the versatility of this platform through applications in reconfigurable metamaterials, deployable arrays, soft robotics, and flexible electronics.