  Let H be a closed, connected subgroup of a connected, simple Lie group G with
finite center. The homogeneous space G/H has a "tessellation" if there is a
discrete subgroup D of G, such that D acts properly discontinuously on G/H, and
the double-coset space D\G/H is compact. Note that if either H or G/H is
compact, then G/H has a tessellation; these are the obvious examples.
  It is not difficult to see that if G has real rank one, then only the obvious
homogeneous spaces have tessellations. Thus, the first interesting case is when
G has real rank two. In particular, R.Kulkarni and T.Kobayashi constructed
examples that are not obvious when G = SO(2,2n) or SU(2,2n). H.Oh and D.Witte
constructed additional examples in both of these cases, and obtained a complete
classification when G = SO(2,2n). We simplify the work of Oh-Witte, and extend
it to obtain a complete classification when G = SU(2,2n). This includes the
construction of another family of examples.
  The main results are obtained from methods of Y.Benoist and T.Kobayashi: we
fix a Cartan decomposition G = KAK, and study the intersection of KHK with A.
Our exposition generally assumes only the standard theory of connected Lie
groups, although basic properties of real algebraic groups are sometimes also
employed; the specialized techniques that we use are developed from a fairly
elementary level.
