A predicted quasicrystal is based on the ‘einstein’ tile known as the hat

The “hat” wowed mathematicians. Now the shape is shaking up physics.

In 2023, mathematicians reported that the 13-sided tile was the first known “einstein.” That’s a shape that can perfectly cover an infinite plane — no gaps or overlaps — but can do so only without a repeating pattern (SN: 3/24/23).

Now, scientists have predicted the properties for a two-dimensional material based on the hat. It’s a quasicrystal, a material that is orderly like a crystal, but in which the arrangements of atoms don’t repeat. Intriguingly, the hat-based material shares properties with graphene, a crystalline material, the researchers report in a paper to appear in Physical Review Letters.

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