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.
IH46

 

      
The template for the IH46 system is any quadrilateral. 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. An example of a template is

                                 Graphic255

A translation cluster is

                           Graphic256

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, an example of each of which is shown. There are no reflection symmetries. The  symmetry group of the tiling is p2.
 
Graphic257

As an example, a shaped tile, based on a design by Escher, can be decorated to look something like a fish as show  

  

Tiles of two different colours suffice to avoid adjacent tiles of the same colour.

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