  As in a symmetric space of noncompact type, one can associate to an oriented
geodesic segment in a Euclidean building a vector valued length in the
Euclidean Weyl chamber; in addition to the metric length it contains
information on the direction of the segment. We study in this paper
restrictions on the vector valued side lengths of polygons in (thick) Euclidean
buildings. The main result is that the set of possible side lengths of n-gons
depends only on the associated spherical Coxeter complex. We show moreover that
it coincides with the space of vector valued weights of semistable weighted
configurations on the Tits boundary.
  The side lengths of polygons in symmetric spaces of noncompact type are
studied in the related paper [KLM1]. Applications of the geometric results in
both papers to algebraic group theory are given in [KLM3].
