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The template for the IH15 system is any hexagon with two adjacent sides equal to one another and with the other two opposite, adjacent sides also equal; the remaining pair of opposite sides must also be equal and parallel. An example is shown below. Only the two pairs of equal adjacent sides can be shaped as indicated by the half-arrows. The template and any tile shape formed from it have an axis of internal reflection symmetry as indicated by the dog pattern.
A translation cluster is
A section of the tiling formed by this same template is shown below, with a translation cluster outlined. The two basic translations are indicated by the the vectors drawn from the highlighted cluster. The tiling has two different centres of two-fold rotational symmetry, as well as two different types of axes of glide and one of mirror reflection symmetry. An example of each of is indicated. The tiling symmetry group is pmg.
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