boost::kruskal_minimum_spanning_tree for a Polyhedron without points

kruskal.cpp

#include <CGAL/Polyhedron_3.h>
#include <boost/graph/graph_traits.hpp>
#include <CGAL/boost/graph/kruskal_min_spanning_tree.h>
#include <CGAL/Simple_cartesian.h>

struct empty {};

struct traits {
    using Point_3 = empty;
    using Plane_3 = empty;
    using Construct_opposite_plane_3 = empty;

    Construct_opposite_plane_3 construct_opposite_plane_3_object() {
        return {};
    }
};

using polyhedron = CGAL::Polyhedron_3<traits>;
//using polyhedron = CGAL::Polyhedron_3<CGAL::Simple_cartesian<double>>;

int main() {
    using vertex_descriptor = typename boost::graph_traits<polyhedron>::vertex_descriptor;
    using vertex_iterator = typename boost::graph_traits<polyhedron>::vertex_iterator;
    using edge_descriptor = typename boost::graph_traits<polyhedron>::edge_descriptor;
    using vertex_index_map = std::map<vertex_descriptor, int>;
    using vertex_index_pmap = boost::associative_property_map<vertex_index_map>;

    // using edge_weight_map = std::map<edge_descriptor, double>;
    // using edge_weight_pmap = boost::associative_property_map<edge_weight_map>;

    using edge_weight_pmap = CGAL::Constant_property_map<edge_descriptor,double>;

    auto poly = polyhedron();
    vertex_index_map index_map;
    vertex_index_pmap index_pmap(index_map);

    // edge_weight_map weight_map;
    // edge_weight_pmap weight_pmap;

    edge_weight_pmap weight_pmap(1.0);

    vertex_iterator vb, ve;
    int index = 0;
    for(boost::tie(vb, ve)=vertices(poly); vb!=ve; ++vb){
        index_pmap[*vb] = index++;
    }
    std::list<edge_descriptor> mst;
    boost::kruskal_minimum_spanning_tree(poly, std::back_inserter(mst), boost::vertex_index_map(index_pmap).weight_map(weight_pmap));

    return 0;
}