Aperiodic Monotile

Hat polykite aperiodic tiling

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile which tiles the plane only aperiodically. It was an open problem for a long time to either find such a tile or show that none exists. The problem was solved by Smith et al. (2023), who found a simple polykite known as a hat that is an aperiodic monotile.

In addition to the hat, Smith et al. (2023) also found a continuum of aperiodic polygonal monotiles.

See also

Aperiodic Tiling, Hat Polykite, Wang's Conjecture

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Pegg, E. "Einstein Problem Solved (Aperiodic Monotile Discovery." Mar 21, 2023., D.; Myers, J. S.; Kaplan, C. S.; and Goodman-Strauss, C. "An Aperiodic Monotile." 20 Mar 2023.

Cite this as:

Weisstein, Eric W. "Aperiodic Monotile." From MathWorld--A Wolfram Web Resource.

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