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.
IH81

 


The template for the IH81 system is a right-angled isosceles triangle as shown below . Only the two equal 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.

                                

A translation cluster consists of eight tiles in different orientations

                          

 A section of the tiling formed by 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 a centre of two-fold and another of four-fold rotation symmetry, two different types of axes of glide and one of mirror reflection symmetry.. An example of each  is indicated. The tiling symmetry group is p4g.
 

From this template we can produce a tile shape in the form of a small animal.

  

Only two different colours are required to avoid the colour of adjacent tiles being the same.
 

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