The template for the IH40 system is a 120° isosceles triangle as shown below. None of the three sides can be shaped. The template and its associated tile have 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 three centres of rotation symmetry, one two-fold,  one two of three-fold and one       six-fold, as well as two axes of mirror and two of glide reflection symmetry. An  example of each is indicated. The tiling symmetry group is p6m.

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 to lower its symmetry.

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

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