  We study finite foldable cubical complexes of nonpositive curvature (in the
sense of A.D. Alexandrov). We show that such a complex X admits a graph of
spaces decomposition. It is also shown that when dim X=3, X contains a closed
rank one geodesic in the 1-skeleton unless the universal cover of X is
isometric to the product of two CAT(0) cubical complexes.
