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Wolfgang
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Timothy Chow
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Aperiodic monotile without reflections?

The recently discovered amazing aperiodic monotile (or "einstein") of David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss tiles the plane only if reflections of the monotile are allowed. Is there hope of modifying their construction to produce an aperiodic monotile that tiles the plane without the need for reflected tiles?