A Geometric Shape That Does Not Repeat Itself When Tiled

IHTFISP shares a report from Phys.Org: A quartet of mathematicians from Yorkshire University, the University of Cambridge, the University of Waterloo and the University of Arkansas has discovered a 2D geometric shape that does not repeat itself when tiled. David Smith, Joseph Samuel Myers, Craig Kaplan and Chaim Goodman-Strauss have written a paper describing how they discovered the unique shape and possible uses for it. Their full paper is available on the arXiv preprint server. [...] The shape has 13 sides and the team refers to it simply as "the hat." They found it by first paring down possibilities using a computer and then by studying the resulting smaller sets by hand. Once they had what they believed was a good possibility, they tested it using a combinatorial software program -- and followed that up by proving the shape was aperiodic using a geometric incommensurability argument. The researchers close by suggesting that the most likely application of the hat is in the arts.

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