Abstract
It is common to fold a hollow 3D Archimedean solid flat using paper folding. However, little has been done to create 3D cellular assemblies of polyhedrons consisting of rigid facets that can be folded flat with a single degree of freedom. Inspired by both origami and kirigami, we present two groups of foldable truncated octahedrons composed of rigidly thin and thick facets, respectively. Starting by identifying seven possible connection types between a pair of foldable truncated octahedrons, we use these connection types to construct various foldable 3D cellular arrays. Kinematically, these arrays contain spherical 4R linkages or a mixture of spherical 4R linkages and Bennett 4R linkages if facets of uniform and finite thickness are used. Through a thorough kinematic analysis, we are able to obtain the relationships amongst all dihedral angles along each folding crease. We demonstrate that the foldable cellular assembly has a single degree of freedom. Moreover, the arrays made from thin and thick facets are kinematically equivalent. Physical models were made, which have successfully validated our findings. The proposed foldable cellular structures can be used to construct space habitats or create robot arms.
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