Spinor

With a grateful nod to G. t'Hooft, and also as described in the Feynman lectures, this is a demonstration of an object that one needs to rotate through 4\pi (two full rotations) to get back to its original state rather than 2\pi (one full rotation). Such objects are called spinors, and play a role in classifying states in quantum mechanics.

Print the box and the star game piece. Tie 4, foot-long threads, each between one of the holes in the ends of the box and a hole in the star game piece in such a way that they are untangled. Done!

To "Play" note that, always keeping the box fixed, if you rotate the star piece around any axis twice the ropes look tangled BUT by simply translating the star piece (without ever rotating it) through the strings in a sequence you can return the strings to their untangled initial state. Not possible if you rotate the star initially just once (2\pi) along any axis!