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.
IH51

 

  
The template for the IH51 system is any quadrilateral with two opposite sides equal in length. All four 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 pattern. An example of a template is

                              

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  two  different centres of two-fold rotation symmetry and two different axes of glide reflection symmetry; an example of each is shown. The symmetry group of the  tiling  is  pgg.
 

From this template we can produce a tile in the form of a fish, based on a design by Escher.

        

To avoid similarly coloured adjacent tiles, two different tile colours are required.

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