  We describe the relationship between dimer models on the real two-torus and
coamoebas of curves in (\CC^\times)^2. We show, inter alia, that the dimer
model obtained from the shell of the coamoeba is a deformation retract of the
closed coaomeba if and only if the number of connected components of the
complement of the closed coamoeba is maximal. Furthermore, we show that in
general the closed coamoeba of the characteristic polynomial of a dimer model
does not have the maximal number of components of its complement.
