Aperiodic Wall Tile Pattern "Monotile"

Aperiodic tiling, folks, is like the 'Jazz' of geometry. It's got some rules but loves to improvise! Picture a floor covered in tiles, but not the kind that make you think, "Oh, I've seen that pattern a million times." No, these tiles are the rebels of the tiling world. They're non-periodic, meaning they don't follow a regular pattern, and they refuse to form big, boring, repetitive patches.

Now, let's talk about the heroes behind this mathematical jazz band – David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. In March 2023, they dropped the mic by proving that David Smith's tile is a bona fide aperiodic monotile. Think of it as solving the unsolved yet Einstein problem of geometry – finding a single shape that can create non-repeating patterns.

But wait, there's a twist in the plot! You see, if you want David Smith's tile to join the aperiodic party, it needs a mirrored buddy. It's like they do the tango together to make the dance non-repetitive. So, in essence, the solo 3D tile dream is a no-go.

I dared make a 3D version of David Smith's ‘aperiodic’ tile! From full-blown diamond shapes to versions with a slice taken out, I've got it all. Sure, you can geek out on these mathematical wonders, but the real magic is turning your space into an accent wall masterpiece. And if you're feeling eco-friendly, the cutaway versions save on materials – double win!

Direction : 
The cutaway versions produce a much better aspect printed upside down. Printing with a single wall and lightning infill is pretty enough for any purpose as the 45° angles makes the parts structurally strong anyways. Be creative, play with heights, colours schemes, colour gradients, I'm looking forward what you guys accomplish. Enjoy !