A friend recently alerted me to this very nifty shape. We decided to tessellate together both the “hat” and “turtle” forms of the tile in order to laser cut them.
Attached are the files we used for cutting. They’re designed for use on a 300x400mm sheet, but the patterns can be repeated as needed for larger areas. They include a curved line through each tile that can be helpful for visualising the aperiodicity of the tiles. The curve is based on a design by Dan Piker
You can see a sample of some of the cut tiles in this Twitter post my friend made!