Supriya Ghosh (Editor)

Tübingen triangle

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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, φ = a b = 1 + 5 2 1.618.

The prototiles are Robinson triangles, but the relation 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.

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 in the patches of the relevant figures.

References

Tübingen triangle Wikipedia