The template for the IH88 system is an equilateral triangle. All three 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.

A translation cluster requires six tiles. An example is

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 three axes of rotation symmetry; one is two-fold, one three-fold and one six-fold. An example of each is shown. The symmetry group of the tiling is p6.
 

The following tile shaped like a fish and based on a design of Escher can be formed

In spite of tiles in six different orientations being required to form a translation cluster, only two colours are required to avoid adjacent tiles having the same colour.

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