The template for the IH87 system is an equilateral 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 formed by six tiles.

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 three different centres of three-fold rotation symmetry, as well as one axis of mirror  reflection and one of glide reflection symmetry. An  example of each  is  indicated. The  tiling  symmetry group is p3m1.

No shaping of the sides of the template is allowed. An example of a tile which can be produced from this template is as follows. It must be decorated internally to show that it has no overall symmetry.

Only two different colours of tiles are required to avoid a clash of adjacent colours in the tiling.

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