The template for the IH23 system is any pentagon with one pair of equal and parallel sides. All five sides can be shaped as indicated by the half-arrows. The template and any  tile shape formed from it have no internal symmetry, as indicated by the dog.

A translation cluster is

A section of the tiling formed by this template is 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 different centres of two-fold rotation symmetry. Its symmetry group is p2.

As an example, the following shaped tile can be formed

Four different colours of tiles tiles are required to ensure no tiles of the same colour are adjacent to one another.

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