Wallpaper group kirigami

TL;DR

This paper establishes a systematic method for designing kirigami structures based on the 17 wallpaper groups, enabling precise control over size and symmetry changes in deployable patterns.

Contribution

It links wallpaper group symmetries to kirigami pattern design, allowing for customizable deployable structures with specific size and symmetry properties.

Findings

Constructed deployable kirigami patterns using all wallpaper groups.

Achieved arbitrary size changes through symmetry-preserving cut patterns.

Connected symmetry control to tile shape and connectivity.

Abstract

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.