  Frieze patterns have attracted significant attention recently, motivated by
their relationship with cluster algebras. A longstanding open problem has been
to provide a combinatorial model for frieze patterns over the ring of integers
modulo $n$ akin to Conway and Coxeter's celebrated model for positive integer
frieze patterns. Here we solve this problem using the Farey complex of the ring
of integers modulo $n$; in fact, using more general Farey complexes we provide
combinatorial models for frieze patterns over any rings whatsoever.
  Our strategy generalises that of the first author and of Morier-Genoud et al.
for integers and that of Felikson et al. for Eisenstein integers. We also
generalise results of Singerman and Strudwick on diameters of Farey graphs, we
recover a theorem of Morier-Genoud on enumerating friezes over finite fields,
and we classify those frieze patterns modulo $n$ that lift to frieze patterns
over the integers in terms of the topology of the corresponding Farey
complexes.
