[abetusk]

The recently discovered 2D "hat" monotile tiles aperiodically but allows reflections (and must allow reflections to tile?).

The paper discusses a (2D) monotile whose shape will allow an aperiodic tiling without reflections.

[alreadydone]

I hope these tables help: https://twitter.com/Junyan_Xu/status/1663396061942038530

[jameshart]

Notably, it's the same authors: David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss