Tiling and crystallography

The image below is of tiling done by Stoyan Smoukov (who kindly provided the image) at a sink in his house.

The tiles have a clever shape so that they can tesselate to fill completely, a two-dimensional surface. Each tile is identical in shape, rather like a shirt with a neck, two sleeves but can have different orientations relative to the axes of the wall, and can have a different colour. But they clearly can be rotated relative to those axes in order to fill space.

The two tiles marked with red squares have exactly the same colour and orientation, but do not represent lattice points because their environments are different, as is evident from the tiles marked with red crosses (these two tiles may be in the same orientation but have different colours.

There is, therefore, no long-range periodicity so the pattern does not qualify as a crystal.