Planar coincidences for N-fold symmetry
- 1 February 1996
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 37 (2) , 1029-1058
- https://doi.org/10.1063/1.531424
Abstract
The coincidence problem for planar patterns with N‐fold symmetry is considered. For the N‐fold symmetric module with NN≥46 is briefly discussed and N=46 is described explicitly. The results of the coincidence problem also solve the problem of colour lattices in two dimensions and its natural generalization to colour modules.Keywords
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This publication has 15 references indexed in Scilit:
- Arithmetic properties of module directions in quasicrystals, coincidence modules and coincidence quasilatticesActa Crystallographica Section A Foundations of Crystallography, 1995
- Root lattices and quasicrystalsJournal of Physics A: General Physics, 1990
- Tables of all coincidence orientations with low multiplicity for arbitrary hexagonal and rhombohedral latticesScripta Metallurgica, 1989
- An icosahedral phase in annealed austenitic stainless steel?Philosophical Magazine Letters, 1989
- Hidden symmetries in general grain boundariesPhilosophical Magazine Letters, 1988
- Beware of 46-Fold Symmetry: The Classification of Two-Dimensional Quasicrystallographic LatticesPhysical Review Letters, 1987
- Pythagoreische Zahlen für den dreidimensionalen RaumPhysikalische Blätter, 1979
- The detection of the periodic structure of high-angle twist boundariesPhilosophical Magazine, 1975
- The detection of the periodic structure of high-angle twist boundariesPhilosophical Magazine, 1975
- Disorientations and coincidence rotations for cubic latticesActa Crystallographica Section A, 1974