The einstein tile: a never-repeating pattern made from a 13-sided shape

The “einstein tile” in action, made up of a unique tridecagon (13-sided shape). David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

From Smithsonian Magazine, via an arXiv paper from 2023:

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

In the paper, the shape is called an aperiodic monotile which refers to its inability to repeat when tiled (aperiodic), and monotile meaning “one-tile”

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