Physics Nature Is Weird

A single, repeating shape can be used to create an infinite variety of materials that fold, twist, and deploy into any mathematical pattern imaginable.

April 24, 2026

Original Paper

Monotile kirigami

arXiv · 2604.19586

The Takeaway

Monotile kirigami structures can be built from a single shape to cover all 17 wallpaper groups and complex quasicrystal patterns. Researchers proved that you don't need a mix of different parts to create shape-morphing materials that can change their size or stiffness. This single-shape approach makes manufacturing these materials much cheaper and easier for industrial use. These structures can be designed to unfold from a flat sheet into complex 3D shapes for use in space antennas or medical stents. It turns the simple art of paper cutting into a universal toolkit for engineering everything from solar sails to deployable shelters.

From the 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 pe