These “Lego blocks” are in the shape of the recently discovered “Einstein Aperiodic Monotile.” An aperiodic tile covers two-dimensional space in such a way as to create infinite patterns that never repeat. Until recently, the existence of an aperiodic monotile was purely theoretical. But here it is!

This shape is intriguing enough to play with in two-dimensions, but these “Lego” blocks let you add another dimension of intrigue and frustration!

See here for video: https://youtu.be/DLJOF8pfeac

This aperiodic tiling requires two mirrored versions of the same shape, provided here as two separate files. You will need to download and print several each to get started. Note that these blocks are not compatible with real Lego

This shape was discovered in March 2023 by mathematicians David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. They refer to the shape as “The Hat.” You can learn more here: https://cs.uwaterloo.ca/~csk/hat/