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The template for the IH31 system is a kite-shaped quadrilateral with two pairs of equal adjacent sides; the sides of one pair are at 120° to one another, and those of the other pair at 60°, 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 from 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 of two-fold, one of three-fold and another of six-fold rotation. An example of each is indicated. The tiling symmetry group is p6.
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