The template for the IH37 system is a rhombus with angles of 60° and 120° as shown below. None of the four sides can be shaped. The template and its associated tile have a centre of two-fold rotation symmetry and two axes 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 different centres of rotation symmetry, one each of two-fold, three-fold and six-fold, as well as two axes of mirror reflection and two of glide reflection symmetry. An example of each is indicated. The tiling symmetry group is p6m.

With no shaping of the template sides being allowed, there is only one tile shape in this system. The tile has the full symmetry of the basic rhombus and needs no decoration. Any decoration applied must not lower the symmetry as in this example.

Three differently coloured tiles are required to avoid a clash of adjacent colours in the tiling.

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