David Smith Einstein Hat 28

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