Symmetries in Origami Metamaterials

Origami crease patterns allow unique control over thin sheets for microscale robotics, enhanced mechanical properties, and mechanical computation. While it is intractable to characterize the mechanical response of crease patterns with generic geometries, most applications rely heavily on crystallographic symmetries to achieve, or prohibit, folding of the sheet. In this talk, I present succinct analytical results that characterize exotic features of periodic origami sheets, from negative Poisson's ratios to topological phases, via such symmetries. These calculations are enabled by a novel formalism where modes are specified by potential-like quantities on the vertices and the symmetries manifest through identification of hopping-like couplings on the edges. I then discuss implications for experimental validation of the theoretical framework and applications for origami metamaterials.