Aperiodic Monotile

This is maths, it's a tile, and now it's a toy :)

You can tile the plane with it. With no gaps.

Any way you tile it, you can never find a repeating pattern that continues paving the plane.

About 50 years after the Penrose tiling's discovery that allowed to tile the plane aperiodically with only two shapes, mathematics researchers David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss, published their finding of a this aperiodic monotile.

To be exact it is a family of shapes, this one, “the hat” is probably the most elegant, it is made of eight “kite” shapes.

This version I designed with paths joining all the long sides (there is one longer side, but it is two aligned shorter sides) just for the beauty of it!

The full paper can be found here :
https://arxiv.org/abs/2303.10798

The 3mf file contains the two filaments swaps, some orientation tweaking to reduce the bridges' lengths, and ironing on all top surfaces.