Funny you mention Rubiks cube, here is a project I worked with 2 fellow computational artists on. We generated the form using open cas.cade, then machined it all on a 5 axis VMC, then assembled with magnets and a steel ball barring that I pulled from a ship engine. Carrol and Ruza if yout out there, I miss you :(
(Especially the multi-dimensional aspect, as I sometimes hang out with people who solve higher-dimensional Rubik's cubes and other similar puzzles!)