The template for the IH80 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 no internal 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. Any tile constructed from it must be decorated internally to indicate that its symmetry is lower than that of its right-angled isosceles triangle shape. As an example, we have

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

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