  Dimension-reduction homogenization results for thin films have been obtained
under hypotheses of periodicity or almost-periodicity of the energies in the
directions of the mid-plane of the film. In this note we consider thin films,
obtained as sections of a periodic medium with a mid-plane that may be
incommensurate; that is, not containing periods other than $0$. A geometric
almost-periodicity argument similar to the cut-and-project argument used for
quasicrystals allows to prove a general homogenization result.
