Einstein Hat Puzzle

In March 2023 a monotile called “The Hat”, that covers an infinite plane aperiodicly was identified by David Smith.

The Puzzle

The puzzle consists of 6 pieces of the Hat and a sliderbox. There are two different sizes available for download, and for each size, there is a flat version and a version with a kite surface structure. The puzzle pieces with kite surface have many acute angles in the first layer and tend to warp, so a good bed grip and levelling are important. The flat Hat pieces are easier and faster to print.

The box can be used as a storage container for the hat tiles since the puzzle is easy to solve. Therefore, a second box is available that contains 5 puzzles on top of each other. The storage box for 5 x 6 puzzle pieces is available for both sizes.

The pieces are used on both sides. The surfaces of the tops or bottoms of the printed puzzle pieces look slightly different. To make the surfaces of the puzzle look even, 3 of the 6 puzzle pieces should be flipped in the slicer.

In addition, the pictures show 4 more symmetrical shapes consisting of 6 Hat tiles and one symmetrical shape consisting of 97 tiles.

3D Printing Tips

The size of the sliding top is crucial. If it's too narrow, the bumps on the top won't snap into place. If it's too wide, the top can usually still be inserted, but it becomes difficult to open.
If the top doesn't fit, it is advisable to adjust its dimensions in the slicer and reprint it. Recommended adjustments are only small increments ranging between approximately 0.2mm and 0.3mm in width (only in width).

Here is a short video explaining this

I printed the puzzle with the following settings:

• Material: PLA
• Resolution: 0.2mm
• Infill: 20%
• no supports
• no raft, no brim

Other

More information about puzzles whose pieces consist of simple geometric shapes (polyforms) can be found at

pentoma.de (german)

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