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The template for the IH81 system is a right-angled isosceles triangle as shown below . Only the two equal 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 consists of eight tiles in different orientations
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 a centre of two-fold and another of four-fold rotation symmetry, two different types of axes of glide and one of mirror reflection symmetry.. An example of each is indicated. The tiling symmetry group is p4g.
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