ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
Using a projection method of de Bruijn [Proc. K. Ned. Akad. Wet. Ser. A (1981), 43, 39–66], Whittaker & Whittaker [Acta Cryst. (1988), A44, 105–112] obtained nonperiodic tilings of the plane with n-fold rotational symmetry, n = 5, 7, 8, 9, 10 and 12. However, when their method was applied to the cases of 3-, 4- and 6-fold rotational symmetry it produced periodic tilings. This might be taken as circumstantial evidence that 3-, 4- and 6-fold rotational symmetry is incompatible with nonperiodicity. It is demonstrated that they are compatible by constructing quasiperiodic tilings with only 3-, 4- and 6-fold rotational symmetry. This approach uses basic eigenvalue methods of matrix theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767391003392
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