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,


The template for the IH8 system is any hexagon with the opposite sides parallel and equal in pairs. All six sides can be shaped as indicated by the half-arrows. The template and any  tile shape formed from it have a centre of two-fold rotation symmetry, as indicated by the dog pattern. An example of a template is


A single template forms its own translation cluster.

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.

As an example, the following shaped tile can be generated


Tiles of four different colours are required to avoid adjacent tiles of the same colour.

 Author - Tom P McLean ---