  We investigate the Tits buildings of the paramodular groups with or without
canonical level structure, respectively. These give important combinatorical
information about the boundary of the toroidal compactification of the moduli
spaces of non-principally polarised Abelian varieties.
  We give a full classification of the isotropic lines for all of these groups.
Furthermore, for square-free, coprime polarisations without level structure we
show that there is only one top-dimensional isotropic subspace.
  In a sequel to this paper we will use this information to establish a general
type result for the moduli space of non-principally polarised Abelian varieties
with full level structure.
