The template for the IH41 system is any parallelogram. All four sides can be shaped as indicated by the half-arrows.  The template and any tile shape formed from it have no internal symmetry, as indicated by the dog.

The tile itself constitutes a translation cluster. A section of the tiling formed by this template is shown below, with a translation cluster outlined.  The two basic translations are indicated by the vectors drawn from the highlighted cluster. The tiling has no rotation or reflection symmetries. Its symmetry group is p1.

As an example, a bird shaped tile, based on a design by Escher, can be formed as shown

Although a single tile forms a translation cluster, two differently coloured tiles are required to ensure no tiles of the same colour are adjacent to one another.

 Author - Tom P McLean --- tom.mclean@virgin.net