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The template for the IH29 system is any pentagon formed by taking an isosceles triangle and using its equal sides as bases on which to mount, on their outsides, two identical right-angled isosceles triangles. An example is shown below with the underlying isosceles triangle indicated by the dotted lines. Only four of the five pentagon sides, viz those forming the triangles' equal sides, can be shaped, but all must be in the same way, as indicated by the half-arrows. The template and any tile shape formed from it have an axis of reflection symmetry as indicated by the dog pattern.
A translation cluster is
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 two types of centres of rotation symmetry, one two-fold and the other four-fold, one type of axis of mirror reflection symmetry and two of glide reflection symmetry. An example of each is indicated. The tiling symmetry group is p4g.
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