  A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete
maximal surface bounded by a lightlike polygon in the Einstein universe
Ein^(1,n) with finitely many vertices. In this article, we give several
characterizations of them. Polygonal surfaces are characterized by finiteness
of their total curvature and by asymptotic flatness. They have parabolic type
and polynomial quartic differential. Our result relies on a comparison between
three ideal boundaries associated with a maximal surface, corresponding to
three distinct distances naturally defined on the maximal surface.
