  In order to classify partial entanglement of multi-partite states, it is
natural to consider the convex hulls, intersections and differences of basic
convex cones obtained from partially separable states with respect to
partitions of systems. In this paper, we consider convex cones consisting of
X-shaped three qubit states arising in this way. The class of X-shaped states
includes important classes like Greenberger-Horne-Zeilinger diagonal states. We
find all the extreme rays of those convex cones to exhibit corresponding
partially separable states. We also give characterizations for those cones
which give rise to necessary criteria in terms of diagonal and anti-diagonal
entries for general three qubit states.
