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Turtle aperiodic monotile "Einstein" — image 1
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Turtle aperiodic monotile "Einstein"

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Model information

Category
Math
License
Creative Commons — Public Domain

This is the turtle variation of the aperiodic monotiles found by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss announced in March 2023. An aperiodic monotile, sometimes called an “einstein,” is a shape that tiles the plane, but never periodically. Because these monotiles are aperiodic, you will find you need to flip over approximately one out of every seven.  This article in Quanta Magazine has a great explanation of the finding and some helpful tips on how to combine the tiles into larger sets to assemble the aperiodic tessellation faster than you can one tile at a time.

I gave them chamfered edges on top and bottom. I recommend slicing with a color change stop halfway, so when you assemble them it will be easy to see which tiles flipped. I also think it's more fun to create patterns with colors, so I printed blue and green turtles with light pink as the flip side. 

I printed on Ankermake M5 with Eryone PLA using 15% gyroid infill and .16mm (optimal) with .4mm nozzle. 

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