Fig. 4: Scatter plot on the inverse-designed mobility of 3D modular origami structures showing reconfigurable structures for various unit cells and mapping sizes; each point represents a combination of geometry and topology of modules.

a Template #1 was obtained using a \(2\times 2\times 2\) mapping of a unit cell consisting of two tetrahedrons and one octahedron, b Template #22 was obtained using a \(2\times 2\times 2\) mapping of a cubic unit cell; and c template #22 was obtained using a \(3\times 3\times 3\) mapping of a cubic unit cell. d Selective sphere reconfigurable structures constructed using template #22 of (c) showing (d) uniaxial extension mode of a modular origami with \({n}_{{bc}}=18\) and \({n}_{{dof}}=6\), and (e) volumetric shrinking mode of a modular origami structure with \({n}_{{bc}}=15\) and \({n}_{{dof}}=4\). \({n}_{c}\) denotes the number of edges in the graph.