Have a Tiling Project and Want to Avoid Repeating Patterns?

[Jim Koepke]

There is a recently discovered shape that can be put together without replication of patterns.

https://www.goodnewsnetwork.org/the-miracle-that-disrupts-order-mathematicians-invent-new-einstein-shape/

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It looks a little like something from M.C. Escher.

For more science in the work > https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/

jtk

[Paul F Franklin]

This is cool! Thanks Jim! I hope someone makes an actual einstein tile in time for me to use it in my upcoming bath remodel.

It would make a pretty cool cutting board too. Cutting the bars would be tricky, but certainly doable with a few fixtures to support them on the saw or CNC.

And it would be a great shape for jigsaw puzzles too; no way to assemble it by shape alone.

[Lee DeRaud]

Google "aperiodic tiling". The 'Einstein' shape is a monotile version, tilings using multiple shapes (AKA 'prototiles') have been around since the '70s.
I'm a fan of the two-shape Penrose version, with rhomboid prototiles that are much easier to mass-produce.
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