1. Cohomology Groups for Spaces of Twelve-Fold Tilings.
- Author
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Bédaride, Nicolas, Gähler, Franz, and Lecuona, Ana G
- Subjects
TILING (Mathematics) ,ORBITS (Astronomy) - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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