  In a symmetric space of noncompact type X = G/K oriented geodesic segments
correspond to points in the Euclidean Weyl chamber. We can hence assign
vector-valued side-lengths to segments. Our main result is a system of
homogeneous linear inequalities describing the restrictions on the side
-lengths of closed polygons. The inequalities are based on the mod 2 Schubert
calculus in the real Grassmannians G/P for maximal parabolic subgroups P.
