News Math

The einstein tile rocked mathematics. Meet its molecular cousin

Chemical properties coax a material to form nonrepeating tiling patterns

In this illustration, a flat plane is made up of orange and red triangles, with smaller molecules within the triangles rotated to create irregular patterns.

This material forms irregular patterns in which the molecules inside one triangle are rotated 60 degrees with respect to those in neighboring triangles. That results in nonrepeating triangular patterns.

Empa

By Zack Savitsky

For centuries, mathematicians and floor designers alike have been fascinated by the shapes that can tile a plane — in particular, those that do so without repetition.

Now, a team of chemists has described a molecule that naturally assembles into these irregular patterns, laying the groundwork for engineering materials that behave differently from regular solids.