Line shellings

Let P be a convex polytope, and let p be a point in the interior of P. We define hyperplane arrangements V(P) and L(P, p), called the visibility arrangement and line shelling arrangement of P. The regions of V(P) correspond to sets of facets of P visible from some point. The regions of L(P, p) correspond to line shellings of P from the point p. If p is "generic," then the matroid defined by L(P, p) is the Dilworth truncation of the matroid of the "projective closure" of V(P). We discuss some special cases, some applications, and some generalizations of these observations.