Tübingen Triangle
The Tübingen triangle is a form of substitution tiling. It is, apart from the Penrose tiling, Penrose rhomb tilings and their variations, a classical candidate to model 5-fold (respectively 10-fold) quasicrystals. The inflation factor is – as in the Penrose case – the golden mean, \varphi=\frac = \frac \approx 1.618. The prototiles are Robinson triangles, but the relationship is different: The Penrose rhomb tilings are locally derivable from the Tübingen triangle tilings. These tilings were discovered and studied thoroughly by a group in Tübingen, Germany, thus the name. They can be obtained by cut-and-project on the 5-cell honeycomb. Since the prototiles are mirror symmetric, but their substitutions are not, left-handed and right-handed tiles need to be distinguished. This is indicated by the colours in the substitution rule and the patches of the relevant figures.E. Harriss (Drawings of 2005-12-01) und D. Frettlöh (Text of 2006-02-27)Tuebingen Triangle. Downloaded on ...
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