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.
IH52

 


The template for the IH52 system is any rectangle. 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.

                                

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, similar to one by Escher, in the form of a bird.

 

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

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