Rotational Symmetries of Platonic Solids

A symmetry of a figure moves a copy of the figure to coincide with its original position. Beside the rotations shown here, the other symmetries of the Platonic solids are reflections in various planes through the center. Symmetries are motions and form a group. If and are symmetries, is also a symmetry: move the figure with , then move the new position with . Try to understand how the rotations shown in this Demonstration combine.