This is Simon Tatham's jigsaw puzzle based on an aperiodic hat tiling discovered in 2023.

A tiling of hats can be morphed continuously into a tiling of turtles, by reversing the ratio of edge lengths, so that the shorter edges become long and the long edges short. In this puzzle, that morph takes place between the top and bottom surfaces, so that each piece has a hat on top and a turtle on the bottom, and the cross-sections in between change shape smoothly from one to the other.

The two tilings are aligned in a way that bounds the distance between corresponding tiles, which means no tile has to lean over too far. The alignment involves scaling and rotation by irrational angles, so despite every piece having the same pair of shapes on top and bottom, no two pieces are the same shape overall.

The tiles are distributed between four STL files, intended to be printed in different colours, plus a fifth file for the frame. This gives the finished puzzle a proper four-colouring (no two adjacent tiles are the same colour), which makes it a bit easier. But you could print it all in the same colour if you prefer it to be harder.

The five files are:

• red.stl: first colour of hat tile

• yellow.stl: second colour of hat tile

• green.stl: third colour of hat tile

• blue.stl: fourth colour, used for the single reflected hat/turtle tile in the puzzle, and also for the inner two-part circular frame

• frame.stl: an outer circular frame in one piece, to hold the whole puzzle together once it's made.

(Of course, you don't have to pay any attention to the colours suggested in the file names. Even my own copy didn't. They're completely arbitrary. Up to you what colours you print it in!)

The code for generating the STL files is available in a Git repository:

git clone https://git.tartarus.org/simon/hat-turtle-jigsaw.git

The files are copyright 2025-2026 Simon Tatham, and the text above is his text with some minor tweaks for context. He has released the source code for generating these files under an MIT licence; that's not an option that's available on Printables, so I'm uploading as CC-BY, since that's a compatible licence and I'm not providing the source code anyway.