  This note defines a complete h-vector for convex polytopes, which extends the
already known toric (or mpih) h-vector and has many similar properties.
Complete means that it encodes the whole of the flag vector.
  First we define the concept of a generalised h-vector and state some
properties that follow. The toric h-vector is given as an example. We then
define a complete generalised h-vector, and again state properties. Finally, we
show that this complete h-vector and all with similar properties will sometimes
have negative coefficients.
  Most of the proofs, and further investigations, will appear elsewhere.
