This is a mirror of Tom McLean's site about isohedral tiling templates. The original website seems to have disappeared. This mirror is hosted by Jaap Scherphuis, jaapsch.net/tilings.
IH68

 


The template for the IH68 system is any rhombus. All  sides of the rhombus 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. An example of a template is

                              

A single tile forms 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 the vectors drawn from the highlighted cluster. The tiling has one axis of glide and one of mirror reflection symmetry, as indicated. The tiling symmetry group is cm.

As an example, the following shape can be formed.

      

The associated tiling requires tiles of two different colours to avoid adjacent tiles  having  the same colour.

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