Multiple planar coincidences with N-fold symmetry

Details Multiple planar coincidences with N-fold symmetry Multiple planar coincidences with N-fold symmetry

2005-11-11

arxiv.org/abs/math/0511306v2

Zeitschrift fuer Kristallographie 221 (2006) 571-581

Mathematics

Metric Geometry

13 pages, two figures. For previous related work see math.MG/0511147 and math.CO/0301021. Minor changes and references updated

Scientific paper

10.1524/zkri.2006.221.8.571

Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results for spectral, combinatorial and asymptotic properties in terms of Dirichlet series generating functions.

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