Why? Consider the red, twelve pointed star lying in the middle of the tiling. This star appears only at the center. This star is not repeated throughout the tiling.

If the tiling were periodic, the star would lie in some fundamental domain for the tiling. Recall that a fundamental domain is a piece of the tiling you can shift around to tile the entire plane. Therefore the star would lie in every periodic parallelogram of the lattice corresponding to the fundamental domain. Obviously, the star cannot appears infinitely many places in the tiling, since it appears only once in the middle of the tiling. (The page about periodic tilings introduces these terms and ideas, if you are feeling a little lost.)