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The template for the IH57 system is any parallelogram. All four sides can be shaped 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 single tile forms a translation cluster.
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 axes of two-fold rotation symmetry, an example of each of which is shown. There are no reflction symmetries. The symmetry group of the tiling is p2.
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