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The template for the IH3 system is any hexagon with a pair of opposite sides equal and parallel to one another; the sides joined to each of these must themselves form equal, non-parallel pairs. All six sides of the hexagon 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. An example of a template is
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 no centres of rotation symmetry but has two different parallel axes of glide reflection symmetry. An example of each is indicated. The tiling symmetry group is pg.
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