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The template for the IH13 system is any hexagon formed by mounting two identical triangles on to opposite sides of a rectangle so that they are mirror images of one another. Note that the triangles can be mounted either externally or internally on to the sides; in the latter case their size must be restricted so that they do not overlap. Examples are shown with both externally and internally mounted triangles with the underlying rectangle outlined with dotted lines. All sides of the hexagon can be shaped as indicated by the half-arrows. The template and any tile shape formed from it have an axis of reflection symmetry as shown by the dog pattern.
A translation cluster based on the first template 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 the vectors drawn from the highlighted cluster. The tiling has two types of centres of two-fold rotation symmetry, 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 pmg.
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