The Hat - An Efficient, Tessellating Cookie Cutter

The "hat" (or "Einstein's Hat" - not affiliated with Albert Einstein) is a geometric shape with a very unique property: it is an aperiodic monotile. This means that like a triangle, square, or hexagon, it can perfectly tile a space with no gaps, however - it does so in a way where the pattern never repeats (aperiodic means there is no translational symmetry).

Like a square or hexagonal cookie cutter, this cookie cutter can cut your dough perfectly, leaving no extra dough in-between the cut-outs and efficiently packed on baking trays. You also have the added benefit of coming across like a mathematician (or huge nerd) when you make these and explain the shape to your friends.

Release Notes: I am currently testing a few different profiles for optimal cookie cutting and print-ease. I believe this current version will work well for both, but stay tuned as the final design may vary slightly from what I have posted now.

Nov 27, 2024 - 
I've added a second model with a different profile. Its 25mm tall, so should be easier to use. Walls are also thicker. Download "v2" for these updates

Interesting article on this shape: https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/
Veritasium video explaining aperiodic tilling (I believe was made before this shape was discovered):