Download Wolfram Notebook

The hat polykite is an aperiodic monotile discovered by Smith et al. (2023).

It is illustrated above in an aperiodic tiling (Smith et al. 2023).

Every tiling by hats uses both handednesses. The same authors later constructed the spectre tile, which admits only nonperiodic tilings of one handedness (Smith et al. 2024).

It is implemented in the Wolfram Language as LaminaData["HatPolykite"].

See also

Aperiodic Monotile, Aperiodic Tiling, Kite, Polykite, Spectre Tile, Tridecagon

Explore with Wolfram|Alpha

References

Pegg, E. "Einstein Problem Solved (Aperiodic Monotile Discovery)." Mar 21, 2023. https://community.wolfram.com/t/21787.Smith, D.; Myers, J. S.; Kaplan, C. S.; and Goodman-Strauss, C. "An Aperiodic Monotile." 20 Mar 2023. https://arxiv.org/abs/2303.10798.Smith, D.; Myers, J. S.; Kaplan, C. S.; and Goodman-Strauss, C. "A Chiral Aperiodic Monotile." Combinatorial Theory 4(2), #13, 1-25, 2024. https://doi.org/10.5070/C64264241. https://arxiv.org/abs/2305.17743.

Referenced on Wolfram|Alpha

Hat Polykite

Cite this as:

Weisstein, Eric W. "Hat Polykite." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HatPolykite.html

Subject classifications