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The hat monotile is a new family of polygons that tiles the plane aperiodically [1]. This Demonstration defines a function that draws the polygon with eight segments of length and six segments of length . The main shape explored has been , since it is four-thirds of a 3-hexagon triangle.

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Contributed by: Ed Pegg Jr (May 8)

Open content licensed under CC BY-NC-SA

## Details

References

[1] D. Smith, J. S. Myers, C. S. Kaplan and C. Goodman-Strauss, "An Aperiodic Monotile." arxiv.org/abs/2303.10798.

[2] E. Pegg. "Einstein Problem Solved (Aperiodic Monotile Discovery)" from Wolfram Community—A Wolfram Web Resource. community.wolfram.com/groups/-/m/t/2861234.

[3] B. Klee. "Hat Tilings via HTPF Equivalence." from Wolfram Community—A Wolfram Web Resource. community.wolfram.com/groups/-/m/t/2858759.

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