I ended up having to read the CGAL source code to figure this one out. There you go. You’re welcome.

#include <CGAL/Inverse_index.h>
#include <CGAL/Polyhedron_3.h>

typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
typedef typename Polyhedron::Vertex_const_iterator VCI;
typedef typename Polyhedron::Facet_const_iterator FCI;
typedef typename Polyhedron::Halfedge_around_facet_const_circulator HFCC;

void write(){
	Polyhedron poly;

	// Your polyhedron code ...

	std::filebuf fb;
	fb.open(outputFile, std::ios::out);
	std::ostream os(&fb);

	os << "ply\n"
	   << "format ascii 1.0\n"
	   << "element vertex " << poly.size_of_vertices() << "\n"
	   << "property float x\n"
	   << "property float y\n"
	   << "property float z\n"
	   << "element face " << poly.size_of_facets() << "\n"
	   << "property list uchar int vertex_index\n"
	   << "end_header\n";

	for (auto it = poly.vertices_begin(); it != poly.vertices_end(); it++){
		os << it->point().x() << " " << it->point().y() << " " << it->point().z() << std::endl;
	}

	typedef CGAL::Inverse_index<VCI> Index;
	Index index(poly.vertices_begin(), poly.vertices_end());

	for( FCI fi = poly.facets_begin(); fi != poly.facets_end(); ++fi) {
		HFCC hc = fi->facet_begin();
		HFCC hc_end = hc;

		os << circulator_size(hc) << " ";
		do {
			os << index[VCI(hc->vertex())] << " ";
			++hc;
		} while( hc != hc_end);

		os << "\n";
	}

	fb.close();
}