The template for the IH71 system is a square as shown below . All four sides can be shaped but all in the same way, as indicated by the half-arrows. The template and any  tile shape formed from it 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 two  types of centres of rotation symmetry, one two-fold and the other four-fold, two different axes of glide and one of mirror reflection symmetry. An example of each is indicated. The tiling symmetry group is p4g.

From this template we can produce a tile shape which is similar to one developed by Escher

Despite the fact that a translation cluster requires four tiles, only two differently coloured of tiles are required to avoid a clash of adjacent colours.

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