The same researchers behind the 13-sided 'hat' shape have stumbled upon a version that improves upon the original in a very important way.
s what’s known as an aperiodic monotile, which means that a single shape can tile a surface without any translational symmetry, or without its pattern ever repeating. The famous
are an example of aperiodic tiling, in which the pattern is aperiodic but uses two different shapes. The hat tiling discovered by the researchers just a few months agouses one shape, except that in order to tile a surface, you’d need to use both the hat and its mirrored reflection—meaning you’d technically need two shapes.
The spectre tiling only uses one shape, an “einstein,” which is German for “one stone,” to completely tile a surface without any part of the pattern repeating. Since the spectre doesn’t need to be reflected like the hat does, the researchers dubbed theAdvertisementThe researchers found a 14-sided shape that, like the hat, could tile a surface without creating repeating patterns as long as its reflection was also used.
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