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The template for the IH42 system is any parallelogram. Only two of the four sides 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 different axes of mirror reflection symmetry. Its symmetry group is pm.
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