Of symmetry planes in a baseball (consider seams)?

Baseball curves have translation symmetry. This means that we can slide a copy of the curve along the surface of the sphere along a straight (great circle) path, and have it line up with another part of the original curve. Notice that if we slide it the shortest distance we can to make it line up, and then slide it again in the same way, the curve is back where it started. For this reason, we say that the curve is periodic with period 2.