Monotile kirigami

TL;DR

This paper demonstrates the creation of deployable kirigami structures based on monotile patterns, covering all wallpaper groups and quasicrystal tilings, with analysis of their shape changes.

Contribution

It provides explicit constructions of monotile kirigami structures, expanding the design space for shape-morphing metamaterials based on simple tilings.

Findings

Constructed periodic monotile kirigami structures for all 17 wallpaper groups.

Developed aperiodic monotile kirigami structures for quasicrystal patterns.

Analyzed shape and size changes of kirigami patterns during deployment.

Abstract

Kirigami, the art of paper cutting, has been widely used in the modern design of mechanical metamaterials. In recent years, many kirigami-based metamaterials have been designed based on different planar tiling patterns and applied to different science and engineering problems. However, it is natural to ask whether one can create deployable kirigami structures based on the simplest forms of tilings, namely the monotile patterns. In this work, we answer this question by proving the existence of periodic and aperiodic monotile kirigami structures via explicit constructions. In particular, we present a comprehensive collection of periodic monotile kirigami structures covering all 17 wallpaper groups and aperiodic monotile kirigami structures covering various quasicrystal patterns as well as polykite tilings. We further perform theoretical and computational analyses of monotile kirigami patterns in terms of their shape and size changes under deployment. Altogether, our work paves a new way for the design and analysis of a wider range of shape-morphing metamaterials.