IH1

 


The template for the IH1 system is any hexagon with its opposite sides equal and parallel to one another. All six 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. An example of a template is

                                

The tile itself constitutes a translation cluster.

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 no rotation or reflection symmetries. Its symmetry group is p1.

As an example, a bird shaped tile can be formed as shown

    

Although a single tile forms a translation cluster, four differently coloured tiles are required to ensure no tiles of the same colour are adjacent to one another.

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