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The template for the IH55 system is a square as shown below. All 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 also shown below, with a translation cluster outlined. The two basic translations are indicated by the vectors drawn from the highlighted cluster. The tiling has three types of centres of rotation symmetry, one two-fold and the others four-fold. An example of each is indicated. The tiling symmetry group is p4.
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