It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile, it can cover an entire surface with no gaps or overlaps but only with a pattern that never repeats.
It’s a surprisingly simple polygon. Before this work, if you’d asked what an einstein would look like, Goodman-Strauss says, “I would’ve drawn some crazy, squiggly, nasty thing.” Other shapes have come close. Taylor-Socolar tiles are aperiodic, but they are a jumble of multiple disconnected pieces — not what most people think of as a single tile. “This is the first solution without asterisks,” says mathematician Michaël Rao of CNRS and École Normale Supérieure de Lyon in France.
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