Spectre Monotile Jigsaw
Description
The Chiral Spectre Aperiodic Monotile is an amazing shape discovered and analyzed in early 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss. It's possible to tile an infinite plane with an infinite number of the same tile, but only aperiodicly; i.e., tiles cannot be arranged in any pattern that repeats forever. The salient feature of this new tile is that all 14 edges are equal length (counting the one double-length side as two edges). Thus, one can curve successive edges alternately, in one style and its converse, to make it "chiral"; i.e., if a file is flipped upside-down, it will not mate to a tile that is right-side-up. I designed this tile's edges in the shape of conventional jigsaw tabs and pockets so that tiles interlock. It's much more satisfying than trying to lay non-interlocking tiles side by side. Placing the tiles makes for a challenging puzzle. It's non-trivial to keep growing a round-ish mat of tiles by adding more around the edges without introducing holes. Any printer bed should fit about 10 tiles at a time when duplicated in the slicer. By default, tiles are 4 mm thick with 15 mm edge length and 0.2 mm of kerf clearance for 3D printing. These parameters can be tuned in the OpenSCAD design or Thingiverse Customizer.
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