Symmetry and dance

If the dancers are allowed only 3 positions of the arms and two positions of the legs, there would be 35 different possible positions. Five of these are symmetrical so if the dancers wear masks on the backs of their heads, rotating through 180 degrees produces a mirror image of the same position. In other words, the dancers have not changed shape.

Each of the 15 asymmetrical positions produces a new one when rotated through 180 degrees. So the dancers would appear to have changed shape.
Moving from one position to any other requires a real change of shape (i.e. a move through at least one other dimension).