  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.
