The template for the IH82 system is a right-angled isosceles triangle as shown below. None of the three sides can be shaped . The template and its associated tile have the full symmetry of the isosceles triangle, ie an axis of reflection symmetry as indicated by the dog pattern.

A translation cluster is

A section of the tiling formed by this template is also shown below, with a translation cluster outlined.  The two basic translations are indicated by  the vectors drawn from the highlighted cluster. The tiling has one centre of two-fold and two of four-fold rotation symmetry, as well as three axes of mirror and one of glide reflection symmetry. An  example of each is indicated. The tiling  symmetry group is p4m..

No shaping of the sides of the template is allowed. Also the template has the full symmetry of an isosceles triangle so that no internal decoration is required.

Only two different colours are required to avoid adjacent tiles having the same colour.

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