I am attempting to do this within CGAL.

From a 3D point cloud, find the convex hull, then loop over the finite facets of the convex hull and print each facet's vertices.

It seems like there should be a straightforward way to do this; I would have expected that 3D polyhedra would own a vector of facet objects, each of which in turn would own a vector of its edges, each of which in turn would own a vector of its vertices, and that their would be some access through this hierarchy using iterators. But so far I have been unable to find a simple way to navigate through this hierarchy (if it exists).