I manufactured a small number of these puzzles for friends and family. If you have one, be aware that there are spoilers on this page.
The day after I placed a large order for “hat” monotile puzzles there was a new announcement from David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, for the aperiodic “spectre” monotile that tiles without reflections (so there really is just one tile):
I knew then that I would be making a second puzzle, this time with “spectre” tiles.
Unlike “hat” tiles, the “spectre” tiles don’t lay out on a regular grid. Where I had manually selected “hat” tiles for the first puzzle by overlaying a hex grid and reading off coordinates, I ended up writing code to automate the coordinate extraction and selection of the “spectre” tiles.
Next, I needed to decide how big to make the “spectre” tiles. I wanted the new puzzle to be the same size as the first, ideally with the same number of pieces (56). I settled on scaling the “spectre” tiles to have the same area as the “hat” tiles in the first puzzle, allowing 56 to fit inside the same sized hexagonal border.
I had concerns about the fragility of the hexagonal border pieces, having so little margin in some places, but went ahead and placed an order with the laser cutting service to have something to play with. Sure enough, one of the border pieces was so fragile it broke during unpackaging.
Nonetheless, it gave me something to play with. The “spectre” puzzle was fun to solve, maybe a little easier than the “hat” puzzle, and I just needed to redesign the border.
Looking at the rotations of the “spectre” tiles, and the angles of their edges, I decided that a dodecagonal (12-sided) border would work better, so I updated the design and ordered some new parts. In fact, I was confident enough to go ahead and place a large order.
The dodecagonal border was much sturdier and, I think, more attractive. It also had the benefit of distinguishing the “spectre” puzzle more from the “hat” puzzle.
I packaged up the new puzzles and sent them off to their new homes.
The insert included with each puzzle points here: https://www.grwster.com/monopuzzle2