September 28, 2023

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A 14-sided shape tiled endlessly without repeating a pattern

Mathematicians are ending a decades-long quest to find the elusive “Einstein’s vampire” figure

What has 14 sides, is full of curves, and can cover a surface without gaps or overlaps? It’s no mystery – it’s “Einstein’s vampire”.

In March, a retired printmaker named David Smith made a remarkable discovery in a scientist mathematics. is found A 13-sided figure that can coat the entire surface without repeating. Nicknamed “The Hat” because of its vaguely fedora-like shape, it was the culmination of decades of hunting by mathematicians around the world.

Since 1961 mathematicians wondered If such a format can exist. First, mathematicians found a set of 20,426 shapes that could be strung together while creating a pattern that never repeats (unlike the tiles on the kitchen floor, which create a repeating pattern). In the end, mathematicians have found a set of 104 shapes that can create a tiling that never repeats.

The middle and right shapes are examples of “spectrums”—shapes with 14 sides that can be tiled infinitely without creating a repeating pattern. (Image credit: Smith et al.)