If you look closely to any tessellation,you will see that it has symmetry in some way; the original motif repeats in a pattern. One possibility is the one shown to your left,which is a whale tessellation. The whales face one way in a line,and then again in the other direction in line. It repeats like this over and over again,eventually creating an amusing tessellation. In some other cases it can have symmetry just as whorl rotating. In all their is seventeen different was you can have symmetry in a flat surface.
Their is also four different way you can your creation around to make a tessellation. To your right is a diagram were Escher and Doris Schattschneider to explain to us how it works. Just like tessellation is related so is symmetry. Symmetry can be very convoluted at times.