  We introduce the notion of a favourable module for a complex unipotent
algebraic group, whose properties are governed by the combinatorics of an
associated polytope. We describe two filtrations of the module, one given by
the total degree on the PBW basis of the corresponding Lie algebra, the other
by fixing a homogeneous monomial order on the PBW basis.
  In the favourable case a basis of the module is parameterized by the lattice
points of a normal polytope. The filtrations induce flat degenerations of the
corresponding flag variety to its abelianized version and to a toric variety,
the special fibres of the degenerations being projectively normal and
arithmetically Cohen-Macaulay. The polytope itself can be recovered as a
Newton-Okounkov body. We conclude the paper by giving classes of examples for
favourable modules.
