David Smith Einstein Hat 28
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28 pieces, all equal. They fit together without gaps and a surprisingly irregular structure. An aperiodic monotile.
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- Source
- Printables
- Category
- Puzzles & Brain-teasers
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- Creative Commons — Attribution — Noncommercial — Share Alike
28 pieces, all equal.
They fit together without gaps, but form a surprisingly irregular structure. It is an aperiodic tiling of the plane.
Roger Penrose made such tilings famous with two or more pieces.
David Smith found a tiling with only one piece, hence the name Einstein.
This puzzle is moderately difficult, when the frame is presented. Fitting pieces into the frame, and working along the outside is a helpful strategy. But eventually the last 3 pieces will not fit. Then you have to rethink your placement, and find variations of the placement.
Included are:
- one svg file, suitable for lasercutting. Green lines for marking the text, red lines to cut pieces and frame.
- freecad file, where the svg was imported and extruded into 3D. These are created with 0.4mm gap between between the pieces, so that a bit of elephant foot or over extrusion is allowed.
- STL files for both Frame and one Hat
- 3MF files created with prusaslicer for Frame + 14 hats, and 14 hats without the frame. Print both (in different colors) to get a complete set.
References:
- https://arxiv.org/abs/2303.10798
- https://en.wikipedia.org/wiki/Einstein_problem
- https://hedraweb.wordpress.com/
- https://cs.uwaterloo.ca/~csk/hat/
- https://www.smithsonianmag.com/smart-news/at-long-last-mathematicians-have-found-a-shape-with-a-pattern-that-never-repeats-180981899/
Category: Puzzles