From Trammell Hudson's Projects
The Platonic Puzzle is a thirteen piece 3D printed puzzle that assembles into into a dodecahedron]. The center piece has a dozen magnets, each of which connects to a pentagonal outside piece. The twelve pentagonal pieces have five magnets in a unique North/South pattern around the outside and one to connect to the center. Since the magnets are not distinguishable by eye, it is necessary to feel how they fit together when assembling the puzzle.
The design is done in OpenSCAD, which makes it easy to do the geometric computation for the shapes. At first I started doing the magnet orientations by hand, but quicklly realized that I needed to write a program to solve them for me. This solver found the unique configuration for the outer pattern.
Since the center section has no rotational symetries, there arepossible configurations of the outer pieces. The puzzle can be assembled in three difficulties: the outer shell alone, the outer shell with the center piece, and a third mode that lines up the outer markings (not yet printed).