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Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of seventeen repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.
Kirigami involves cutting a flat, thin sheet that allows it to morph from a closed, compact configuration into an open deployed structure via coordinated rotations of the internal tiles. By recognizing and generalizing the geometric constraints that
Kirigami, the art of introducing cuts in thin sheets to enable articulation and deployment, has till recently been the domain of artists. With the realization that these structures form a novel class of mechanical metamaterials, there is increasing i
Modified group projector technique for induced representations is a powerful tool for calculation and symmetry quantum numbers assignation of a tight binding Hamiltonian energy bands of crystals. Namely, the induced type structure of such a Hamiltoni
We present a theorem on the compatibility upon deployment of kirigami tessellations restricted on a spherical surface with patterned cuts forming freeform quadrilateral meshes. We show that the spherical kirigami tessellations have either one or two
How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use