June 12, 2023
Description
This is a 3D model of the world's first "einstein", an aperiodic monotile.
Update: There's a chiral (handed) aperiodic monotile now, see: https://www.printables.com/model/494205-spectre-worlds-first-chrial-aperiodic-monotile
You will likely have seen various examples of https://en.wikipedia.org/wiki/Tessellation , endless patterns made up of only a few or even just one single tile. You may also have seen https://en.wikipedia.org/wiki/Penrose_tiling , an endless pattern which can never repeat, based on only two tiles.
In 2023, the https://en.wikipedia.org/wiki/Einstein_problem (from German “one stone”, but also a play of words on a certain scientist) was solved for the first time: Is there a single geometry which allows for perfect tessellation in a pattern that will never repeat? The answer is (likely, the paper still needs peer review as of 2023-03-22) yes: https://arxiv.org/pdf/2303.10798.pdf
Feel invited to print a few billions pieces to try it for yourself.
And please: Upload as many makes with as many pieces in as many colors as you can.
The measurements are precise to micrometers; 1.73 =~ sqrt(3), an irrational number. The physical model is not perfect in the mathematical and it can never be. In practice, this does not matter; warping of your prints and other imperfections will become a problem way before you manage to print an infinite amount of pieces.
If your printer makes imperfect corners, consider printing the fillets version; all corners have a 0.5mm radius fillet in those models.
Extra / fun files:
If you want to learn more about penrose tiling, there's a few nice videos on YouTube:
License:
Creative Commons — Attribution
RichiH
