File:Tübinger Dreieck.gif

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Tübinger_Dreieck.gif (316 × 516 pixels, file size: 8 KB, MIME type: image/gif)

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English: Apart from the Penrose rhomb tilings (and their variations), this is a classical candidate to model 5-fold (resp. 10-fold) quasicrystals. The inflation factor is - as in the Penrose case - the golden mean, sqrt(5)/2 + 1/2. The prototiles are Robinson triangles, but these tilings are not mld to the Penrose tilings. 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.[1]

Since the prototiles are mirror symmetric, but their substitutions are not, we have to distinct left-handed and right-handed tiles. This is indicated by the colours in the substitution rule and in the patch below.

Text by D. Frettlöh
Date
Source Tuebingen Triangle on Tilings Encyclopedia - In rhombs, and wedges, and half-moons, and wings (Images: E. Harriss; Text: D. Frettlöh)
Author E. Harris

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This file is licensed under the Creative Commons Attribution 2.0 Generic license.
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  1. 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

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current20:42, 5 March 2015Thumbnail for version as of 20:42, 5 March 2015316 × 516 (8 KB)NearEMPTiness (talk | contribs)User created page with UploadWizard

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