  The aim of this work is to prove that the connected parts of Farey complex
structure in plane are triangles or quadrangles. To do this work we go back to
plane convex polygones with oriented edge for wich we prove that if two
consecutive vectors of the edge never are in the same quadrant, then the
polygone is a triangle or a quadrangle. Then we prove that the connected parts
of Farey complex have this property.
