I ended up having to readÂ 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(); }0