A wide range of engineering applications, ranging from civil to space structures, could benefit from the ability to construct material-efficient lattices that are easily reconfigurable. The challenge preventing modular robots from being applied at large scales is mainly the high level of complexity involved in duplicating a large number of highly integrated module units. We believe that reconfigurability can be more effectively achieved at larger scales by separating the structural design from the rest of the functional components. To this end, we propose a modular chainlike structure of links and connector nodes that can be used to fold a wide range of two-dimensional (2D) or three-dimensional (3D) structural lattices that can be easily disassembled and reconfigured when desired. The node geometry consists of a diamondlike shape that is one-twelfth of a rhombic dodecahedron, with magnets embedded on the faces to allow a forceful and self-aligning connection with neighboring links. After describing the concept and design, we demonstrate a prototype consisting of 350 links and experimentally show that objects with different shapes can be successfully approximated by our proposed chain design.