This is something of a tangent, but this is kind of a cool visualization of what is sometimes called a "spinorial" object -- an object which can undergo a full

This is something of a tangent, but this is kind of a cool visualization of what is sometimes called a "spinorial" object -- an object which can undergo a full rotation and yet not come back to its original state. Here the number of rotations necessary to restore the original state depends on the number of teeth on the gears. A more classic spinorial object is a belt attached to, say, a book, or apparently your own arm holding up an oriented plate: http://en.wikipedia.org/wiki/Plate_trick http://en.wikipedia.org/wiki/Plate_trick