Monotile kirigami

2026-04-21

AI Summary

This study investigates the construction of deployable kirigami structures based on monotiles. Through explicit geometric design, combined with group-theoretical classification, theoretical analysis, and computational simulations, the authors systematically develop periodic kirigami patterns that span all 17 wallpaper groups and, for the first time, realize a variety of aperiodic monotile-based kirigami—including quasicrystalline and polykite tilings. The work not only establishes the existence of both periodic and aperiodic monotile kirigami but also uncovers the deformation mechanisms and scaling behaviors inherent in their deployment processes. These findings substantially expand the design space for morphing metamaterials.

Technology Category

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Application Category

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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.

Problem

• monotile
• kirigami
• metamaterials
• tiling patterns
• deployable structures

Innovation

• monotile kirigami
• wallpaper groups
• aperiodic tiling
• shape-morphing metamaterials
• quasicrystal patterns