Polytope structures for Greenberger-Horne-Zeilinger diagonal states

We explore the polytope structures for genuine entanglement, biseparability and full biseparability of multi-qubit GHZ diagonal states. We show that biseparable GHZ diagonal states make hypersimplices, and fully biseparable states make the convex hulls of simplices and cubes. We also compute precise volumes for genuine entanglement, biseparability and full biseparability among all GHZ diagonal states.