Tübingen triangle
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/93/T%C3%BCbinger_Dreieck.gif/170px-T%C3%BCbinger_Dreieck.gif)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/T%C3%BCbinger_Dreiecke.gif/220px-T%C3%BCbinger_Dreiecke.gif)
The Tübingen triangle is a form of substitution tiling. It 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,
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.[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
[edit]References
[edit]- ^ 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. Archived 2015-04-02 at the Wayback Machine Downloaded on 2015-03-06.