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The template for the IH67 system is any trapezium, with its non-parallel sides equal in length. Only these non-parallel sides can be shaped and this must be done in the same way, 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 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 as well as two different axes of glide reflection and two of mirror reflection symmetry; an example of each is shown. The symmetry group of the tiling is cmm.
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