Swirling movements, popular among contemporary dancers and choreographers, often embody double rotations of the limbs similar to the Dirac plate or belt trick, in which an object attached to a stationary body by a flexible cord returns to its original state after a rotation of not 360° but 720°. This phenomenon is also seen in the Balinese candle dance, baton twirling, poi, and other performance forms. It is efficiently modeled by the quaternions and illustrates the mathematical theorem that the group SU(2) double covers the rotation group SO(3). We will look at how this plays out in dance and other performing arts, give some suggestions for simple and enjoyable movement tasks that illustrate the concepts, and see how comprehending the embodiment of the quaternions helps us better understand both the mathematics and the relevant movement arts.