In:
International Mathematics Research Notices, Oxford University Press (OUP), Vol. 2022, No. 18 ( 2022-09-12), p. 14181-14254
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.
Type of Medium:
Online Resource
ISSN:
1073-7928
,
1687-0247
DOI:
10.1093/imrn/rnab117
Language:
English
Publisher:
Oxford University Press (OUP)
Publication Date:
2022
detail.hit.zdb_id:
1465368-0
SSG:
17,1
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