  We consider here square tilings of the plane. By extending the formalism
introduced in [3] we build a correspondence between plane maps endowed with an
harmonic vector and square tilings satisfying a condition of regularity. In the
case of periodic plane square tiling the relevant space of harmonic vectors is
actually isomorphic to the first homology group of a torus. So, periodic plane
square tilings are described by two parameters and the set of parameters is
split into angular sectors.
  The correspondence between symmetry of the square tiling and symmetry of the
plane maps and harmonic vectors is discussed and a method for enumerating the
regular periodic plane square tilings having r orbits of squares is outlined.
