A Chiral Aperiodic Monotile

An update to the aperiodic tile. This update shows that a shape that tiles the plane aperiodically without reflections is possible. The original one did not.

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Mathematicians have finally discovered an elusive ‘einstein’ tile

A 13-sided shape known as “the hat” has mathematicians tipping their caps.

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.

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With Discovery, 3 Scientists Chip Away At An Unsolvable Math Problem

There are now 15 known convex pentagons, or nonregular pentagons with the angles pointing outward, that can "tile the plane."

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