This is a question about the einstein problem. As has been well known, in 2023, work of
David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss (https://arxiv.org/abs/2303.10798) showed the First example of an aperiodic monotile (see picture below). As you can see, this example is not convex. Is there any theorem in tiling that implies no convex aperiodic monotile exists?
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