  Given a hypersurface coamoeba of a Laurent polynomial f, it is an open
problem to describe the structure of its set of connected complement
components. In this paper we approach this problem by introducing the lopsided
coamoeba. We show that the closed lopsided coamoeba comes naturally equipped
with an order map, i.e. a map v from its set of connected complement components
to a translated lattice inside the zonotope of a Gale dual of the point
configuration supp(f). Under a natural assumption, the map v is a bijection.
Finally we use this map to obtain new results concerning coamoebas of
polynomials of small codimension.
