Electronic Resource
[S.l.]
:
International Union of Crystallography (IUCr)
Acta crystallographica
46 (1990), S. 962-970
ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
The grid method has been used to calculate the frequencies of the different vertices and corresponding Voronoi polygons occurring in generalized Penrose patterns. A simplified purely geometrical description of the importance of the Σ γj = 0 (mod 1) relation for Penrose patterns that obey certain necessary matching conditions is given. In n-grids with n odd, local 2n-fold symmetry occurs only if the inequality n cos α/(1 + cos α) (mod 1) 〈 Σ γj 〈 n/(l + cos α) (mod 1), where α = π/n, is fulfilled. n-grids and their corresponding rhombus patterns show global 2n-fold symmetry if Σ γj = 1/2 (mod 1), where γj = 1/2 (mod 1).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767390008479
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