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.
IH39

 

 

 The template for the IH39 system is an isosceles triangle with a120° angle   as shown below. All three 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

                  

A translation cluster is
                      

A section of the tiling formed from this template is also shown below, with a translation cluster outlined.  The two basic translations are indicated by  the vectors drawn from the highlighted cluster. The tiling has three  types of centres of rotation symmetry, one of two-fold, one of    three-fold and another of six-fold rotation. An example of each is indicated. The tiling symmetry group is p6.

From this template we can produce the following bird-like tile


  Graphic

Three different colours are required to avoid adjacent tiles having the same colour.

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