The template for the IH72 system is a rectangle as shown below. None of the four sides can be shaped. The template and its associated tile have the full symmetry of a rectangle, ie two-fold rotation symmetry and two axes of reflection symmetry as  indicated by the dog pattern.

A single tile forms the translation cluster.

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 four centres of two-fold rotation symmetry, and four axes of mirror reflection symmetry. An example of each  is  indicated. The tiling symmetry group is pmm.

No shaping of the template sides is allowed, and as the template has the full symmetry of a  rectangle, no decoration of the rectangle is required to define a lower level of symmetry. If any decoration is used it must not lower the rectangular symmetry, as shown in this example.

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