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- W3172214183 abstract "Abstract We consider tilings of the plane with twelve-fold symmetry obtained by the cut-and-projection method. We compute their cohomology groups using the techniques introduced in [ 9]. To do this, we completely describe the window, the orbits of lines under the group action, and the orbits of 0-singularities. The complete family of generalized twelve-fold tilings can be described using two-parameters and it presents a surprisingly rich cohomological structure. To put this finding into perspective, one should compare our results with the cohomology of the generalized five-fold tilings (more commonly known as generalized Penrose tilings). In this case, the tilings form a one-parameter family, which fits in simply one of the two types of cohomology." @default.
- W3172214183 created "2021-06-22" @default.
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- W3172214183 date "2021-06-02" @default.
- W3172214183 modified "2023-10-16" @default.
- W3172214183 title "Cohomology Groups for Spaces of Twelve-Fold Tilings" @default.
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- W3172214183 doi "https://doi.org/10.1093/imrn/rnab117" @default.
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