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Abstract
The paper presents a strict mathematical proof of the classifications of finite groups of symmetries of two-dimensional quasicrystals given by Hermisson, Richard and Baake in 1997.
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Acknowledgements
We thank Prof. E.S. Golod for useful consultations concerning cyclotomic fields and the referees for their valuable comments and remarks. This research was partially supported by grants RFBR 06-01-00037, NSh-5666.2006.1.