Spyke

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"The Hat", a shape that tiles but never makes a repeating pattern

When these went viral in 2022 I read the research paper and found out that not only do they form a non-repeating pattern, but that non-repeating pattern relies on the occasional tile being reversed. That inspired me to 3D print a bunch of these that were a different color on each side and try assembling them. It's very interesting, because you have a lot of options for how to put them together, but occasionally you'll hit a point where the pattern itself forces you to put one in upside down, even though it's non-repeating. Also, it's possible to put it together "wrong" where at one edge you can't add any more tiles in either orientation and have to disassemble part of it to continue. Very interesting to mess with.

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It's janky AF

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