Tübingen triangle
The Tübingen triangle is, apart from the 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, [math]\displaystyle{ \varphi=\frac{a}{b} = \frac{1 + \sqrt{5}}{2} \approx 1.618. }[/math]
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.[1]
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.[2]
See also
References
- ↑ Baake, M and Kramer, P and Schlottmann, M and Zeidler, D Planar patterns with fivefold symmetry as sections of periodic structures in 4-space Internat. J. Modern Phys. B, 1990, 4, 15–16, pp. 2217–2268, 92b:52041
- ↑ E. Harriss (Drawings of 2005-12-01) und D. Frettlöh (Text of 2006-02-27): Tuebingen Triangle. Downloaded on 2015-03-06.
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