The template for the IH32 system is a kite shape with angles of 60° and 120° as shown below. None of the four 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 different centres of rotation symmetry, one two-fold, one three-fold and one 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.

No shaping of the sides of the template is allowed. Also the template has the full symmetry of a kite as indicated by the dog pattern, so that no internal decoration is required to further define tile symmetry.

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

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