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.
IH60

 


The template for the IH60 system is a rectangle as shown below. None of the four sides can be shaped, but in spite of that the template does not have the full symmetry of a rectangle, as can be seen from the half-arrow markings and the dog pattern; it has only an axis of two-fold rotation symmetry. Any tile formed from the template can only be rectangular and its symmetry must be lowered from that of its rectangular shape by appropriate internal decoration.

                                

A translation cluster is

                                

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 four centres of two-fold rotation symmetry, and two axes of mirror and two of glide reflection symmetry. An example of each is indicated. The tiling symmetry group is cmm.

Lowering the symmetry of a rectangular tile is achieved by the following type of decoration

                

Only two different colours of tiles are required to avoid a clash of adjacent colours in the tiling.
 

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