  Convex polytopes are convex hulls of point sets in the $n$-dimensional space
$\E^n$ that generalize 2-dimensional convex polygons and 3-dimensional convex
polyhedra. We concentrate on the class of $n$-dimensional polytopes in $\E^n$
called sign permutation polytopes. We characterize sign permutation polytopes
before relating their construction to constructions over the space of quantum
density matrices. Finally, we consider the problem of state identification and
show how sign permutation polytopes may be useful in addressing issues of
robustness.
