The hat tile (solution of the Einstein problem)

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The hat tile (solution of the Einstein problem)

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A1 mini
P1S
P1P
X1
X1 Carbon
X1E
A1

0.2mm layer, 2 walls, 12% infill
0.2mm layer, 2 walls, 12% infill
1.4 h
2 plates

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Description

The Einstein problem is a mathematical problem from discrete geometry. A geometric shape is sought that can be joined together in rotated, shifted and/or mirrored copies without overlapping, so that the entire plane is covered (parquetized) without gaps. In addition, this form should have the property that no parquetry with a periodically recurring pattern - as on wallpaper - can be created. The problem was considered unsolved for decades; two solutions were proposed for the first time in 2023. The name of the problem is a humorous reference to Albert Einstein and states that only one shape ("one stone") should parquet the plane.

 

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