The template for the IH2 system is any hexagon having two opposite sides both equal and parallel to one another, and the sides within each of the two remaining pairs of adjacent sides also equal to one another. All six sides can be shaped as indicated by the half-arrows. The temp late and any tile shape formed from it have no internal symmetry, as indicated by the dog. An example of a template is

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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 different axes of glide reflection symmetry; an example of each is shown. The  symmetry group of the tiling is  pg.
 

As an example, a shaped tile, based on a design by Escher and which, with decoration, can be made to look like a bird and fish side by side  is

Two different colours are required in the tiles, one for the bird and one for the fish to avoid tiles of the same colour being adjacent to one another.

At first sight this tiling may not seem to be isohedral as a result of apparently two different tile shapes. However the bird and fish shapes are inextricably bound together and together form the single repeating tile shape. Another example like this can be found at IH53.

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