Pavel's Puzzle Blog

Last year, my puzzle-design mind kept drifting to polyhedra, specifically to ways for pieces representing the faces of polyhedra to connect and interact with one another at each edge. My Octamaze and Gamesters of Triskelion puzzles came out of this realm, and for my IPP 2008 Exchange puzzle, I wanted to move up from the octahedron to my favorite of the Platonic solids, the dodecahedron. My experience with the tab-and-slot mechanism of the earlier puzzles, though, had made me very dubious that such an approach would continue to work for the rather larger dihedral angle of the dodecahedron: the tab would be coming into the slot at such a shallow angle that the slot would have to be quite wide, and the piece deformation needed to insert the last face probably wouldn't work at all, let alone elegantly.

I also wanted to use a prettier material than the opaque black high-impact polystyrene I'd used before, and that ruled out pretty much any piece deformation at all. (I'd tried making Octamaze out of acrylic, since it takes etching much better than polystyrene does, but after having my acrylic prototype shatter in my hands during disassembly, I gave up and went with the much more robust and pliant polystyrene.)

I decided that the pieces would rotate into position, using some kind of interlocking, hook-shaped protrusions on the edges of each face; that would still entail fairly wide (deep?) hooks, due to the shallow angle, but avoid any piece deformation during assembly. I realized that I might run into a mechanical problem with the corners of the faces hanging up on one another as each face was rotated into position, so I started considering various piece shapes that were missing the face corners. I started playing around with actual shapes on paper, instead of just thinking about all of it, and all of this came together in a kind of practical lesson in geometric duality: the hooks would be on the ends of arms, and the puzzle would look like stars with interacting points rather than the regular polygonal faces I'd originally imagined.

The resulting puzzle is probably the prettiest one I've ever designed, once assembled: it would make a great Christmas ornament, or an attractive object to dangle from the rear-view mirror of your car, let alone just sitting on your desk at work. It's also quite a difficult puzzle, so keep that in mind if you buy a copy. Like all of my puzzles, it comes with the solution, though, so nobody need know if you decide to short-circuit the solving and jump to the pretty bit.

[Update 8/27/2011: I've renamed this puzzle to "Crystal Ball", which I think describes it better than the old name, not to mention avoiding potential trademark issues... :-)]