  In tri-partite systems, there are three basic biseparability, $A$-$BC$,
$B$-$CA$ and $C$-$AB$ biseparability according to bipartitions of local
systems. We begin with three convex sets consisting of these basic biseparable
states in the three qubit system, and consider arbitrary iterations of
intersections and/or convex hulls of them to get convex cones. One natural way
to classify tri-partite states is to consider those convex sets to which they
belong or do not belong. This is especially useful to classify partial
entanglement of mixed states. We show that the lattice generated by those three
basic convex sets with respect to convex hull and intersection has infinitely
many mutually distinct members, to see that there are infinitely many kinds of
three qubit partial entanglement. To do this, we consider an increasing chain
of convex sets in the lattice and exhibit three qubit
Greenberger-Horne-Zeilinger diagonal states distinguishing those convex sets in
the chain.
