  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.
