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The template for the IH78 system is any right-angled triangle. Only the hypotenuse 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 four different centres of two-fold rotation symmetry, two different axes of mirror and two of glide reflection symmetry. Examples of each are shown. The symmetry group of the tiling is cmm.
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