David Smith Einstein Hat 28

thingiverse

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/