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The template for the IH49 system is any trapezium. Only the two non-parallel 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 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 different centres of two-fold rotation symmetry, two different axes of glide and one of mirror reflection symmetry. Examples of each are shown. The symmetry group of the tiling is pmg.
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