The template for the IH63 system is a square 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 square, as can be seen from the half-arrow markings and the dog pattern; it has only an axis of four-fold rotation symmetry. Any tile formed from the template can only be square and its symmetry must be lowered from that of its square 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 one centre of two-fold and one of four-fold rotation symmetry, as well as an axis of mirror reflection and two of glide reflection symmetry. An  example of each  is  indicated. The tiling symmetry group is p4g.

An example of a tile shape which can be produced from this template is as follows. The tile must be decorated internally to indicate its lower symmetry than that of its square shape.

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

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