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The hat tile (solution of the Einstein problem) – 3D printable model from MakerWorld MakerWorld
Mathematics

The hat tile (solution of the Einstein problem)

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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.
Category
Mathematics
Source
MakerWorld
Published
Updated
What you need to print this: Beginner Low confidence
Single piece
Supports 1/3
Assembly 0/3
Settings 1/3
Bed size 0/3
Post-process 0/3
Printer
FDM / FFF
File format
STL
Material
PLA
Software
Cura, PrusaSlicer, or similar
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