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The template for the IH59 system is any rhombus. All sides of the rhombus can be shaped, but all in the same way, as indicated by the half-arrows. The template and any tile shape formed from it have a centre of two-fold rotation symmetry as indicated by the dog pattern.
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 the vectors drawn from the highlighted cluster. The tiling has two different centres of two-fold rotation symmetry and two different axes of glide reflection symmetry, as indicated. The tiling symmetry group is pgg.
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