Researchers uncover the mathematical structure behind mesmerizing tiling patterns, linking their visual appeal to the ...

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The pentagon is not a shape you typically see used for tiling. Take a peek at your average bathroom tile pattern and you’ll probably see triangles, quadrilaterals, or hexagons–shapes that, when ...

The recently discovered “hat” aperiodic monotile admits tilings of the plane, but none that are periodic [SMKGS23]. This polygon settles the question of whether a single shape—a closed topological ...

There is a shape called “the hat” that can completely cover a surface without ever creating a repeating pattern. For decades, mathematicians had wondered whether a single tile existed that could do ...