If we have all coordinates of the vertices of an arbitrary polyhedron, is it possible to determine on what faces they are and in what order?
Actually, I already know the first part of the question, because I did it using linear programming. Therefore, what I really need to determine is the order of the vertices on each face. Thanks.
If the polyhedron is non-convex, then no: Take the four vertices of a tetrahedron and add a fifth vertex inside their convex hull.