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The template for the IH30 system is a kite-shaped quadrilateral with two pairs of equal adjacent sides; in one pair the sides are at 120° to one another, and in the other pair at 60°, as shown below. Only the sides at 120° 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 two types of centres of three-fold rotation symmetry, as well as an axis of glide and another of mirror reflection symmetry. An example of each is indicated. The tiling symmetry group is p31m.
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