Triangulating a point set using boost::polygon::voronoi results in overlapping triangles

Question

I'm triangulating a set of 2d points using boost::polygon::voronoi and the code below (found under this question)

boost::polygon::voronoi_diagram<vert_value_typed> vd{};
boost::polygon::construct_voronoi(vertices.begin(), vertices.end(), &vd);
for (const auto& vertex : vd.vertices()) {
    boost::container::static_vector<uint32_t, 40> big_face{};
    const auto* start_edge = vertex.incident_edge();
    auto* edge = start_edge;
    do {
        const auto cell = edge->cell();
        ASSERT(cell && cell->contains_point());
        big_face.push_back(util::checked_cast<uint32_t>(cell->source_index()));
        if (big_face.size() == 3) {
            // process output triangles
            faces.push_back({
                big_face[0],
                big_face[1],
                big_face[2]
            });
            big_face.erase(big_face.begin() + 1);
        }
        edge = edge->rot_next();
    } while (edge != start_edge);
}

However, some of my triangles overlap as illustrated by the following image:

Note that the overlapping triangles always have a reversed culling compared to the rest, i.e they are pointing downwards.

How can I modify the algorithm so that the resulting mesh does not contain these overlapping images? I'm not fluent enough in voronoi diagrams to solve this manually.