The template for the IH27 system is any pentagon with two pairs of non-adjacent sides, in which the sides in each pair are equal to one another and make equal and opposite angles with a direction common to both pairs. All five sides of the pentagon can be shaped as indicated by the            half-arrows. The template and any tile shape formed from it have no internal symmetry, as indicated by the dog.

A translation cluster is

 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 two centres of two-fold rotation symmetry and two orthogonal axes of glide reflection symmetry. An example of each  is indicated. The tiling symmetry group is pgg.
 

A tile in the shape of a dog, based on a design of Escher, can be formed as follows

This form of the template, although unusual with two of the pentagon's sides being extensions of one another, nevertheless satisfies the required constraints. The consequent tiling requires dogs of four different colours to avoid adjacent colours being the same.

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