Plate trick

To say that SU(2) double-covers SO(3) essentially means that the unit quaternions represent the group of rotations twice over.

[6] As with the plate trick, these particles' spins return to their original state only after two full rotations, not after one.

The same phenomenon can be demonstrated using a leather belt with an ordinary frame buckle, whose prong serves as a pointer.

The surprise element of the trick is that a second 360° turn in the clockwise direction, while apparently making the belt even more twisted, does allow the belt to be returned to its untwisted state by maneuvering the buckle under the clamped end while always keeping the buckle horizontal and pointed in the same direction.

[3] The belt trick has been theoretically constructed in 1-d Classical Heisenberg model as a breather solution.