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