The fact that the fundamental group SO(3) is Z/2 is sometimes shown by a funny
movement of the arm, twisting it once while keeping the hand palm up, and detwisting
it by twisting it once more.
See also [this thread][1] on Stackexchange.

  [1]: http://math.stackexchange.com/questions/17856/visualizing-the-fundamental-group-of-so3