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.
IH16

 

  
The template for the IH16 system is any hexagon having four equal adjacent sides, those in the first pair and in the second pair making angles of 120° with one another; the remaining adjacent sides are also equal to, and make an angle of 120° with one another. An example is shown below. Only the first four of the six sides can be shaped, as indicated by the half-arrows. The template and any tile shape formed from it have an axis of reflection  symmetry as indicated by the dog pattern.

                                

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 two  types of centres of three-fold rotation symmetry, as well as an axis of glide and another of mirror reflection symmetry. An example of each is indicated. The tiling symmetry group is p31m.

From this template we can produce the following  tile in the shape of a face

        

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

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