The template for the IH34 system is a rhombus with angles of 60° and 120° as shown below. All four sides can be shaped but all in the same way, 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 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 a tile shape which in itself seems of little interest, but when appropriately coloured in its different orientations in the associated tiling, it produces an interesting three dimensional effect of steps.

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

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