  We explore the polytope structures for genuine entanglement, biseparability,
full biseparability and Bell inequality of multi-qubit GHZ diagonal states. We
first show that biseparable GHZ diagonal states make hypersimplices inside the
simplices consisting of all GHZ diagonal states. Next, we consider full
biseparability which is equivalent to positive partial transpose for GHZ
diagonal states, and show that they make the convex hulls of simplices and
cubes. We also visualize which part of the simplex violates multipartite Bell
inequality. Finally, we compute precise volumes for genuine entanglement,
biseparability, full biseparability and states violating Bell inequality among
all GHZ diagonal states.
