The connection between symmetry and degeneracy (that is, the fact that apparently unrelated quantities turn out to be equal) is familiar in every day experience. Consider a simple example, where we draw three points on a plane, and calculate the distance between each of the three points. If the points are placed randomly, then in general all of these distances will be different. However, if the points are arranged so that a rotation by 120 degrees leaves the picture invariant, then the distances between them will all be equal (as this situation describes an equilateral triangle). The observed degeneracy boils down to the fact that the system has a D 3 symmetry.