diff --git a/Convex_hull_3/include/CGAL/convex_hull_3.h b/Convex_hull_3/include/CGAL/convex_hull_3.h
index 70038f9c9c5..8bd566aeaa8 100644
--- a/Convex_hull_3/include/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/include/CGAL/convex_hull_3.h
@@ -315,13 +315,26 @@ void coplanar_3_hull(InputIterator first, InputIterator beyond,
 
   typename boost::property_map<Polyhedron_3, CGAL::vertex_point_t>::type vpm
     = get(CGAL::vertex_point, P);
-  std::vector<typename boost::graph_traits<Polyhedron_3>::vertex_descriptor> vertices;
+  typedef boost::graph_traits<Polyhedron_3> Graph_traits;
+  typedef typename Graph_traits::vertex_descriptor vertex_descriptor;
+  typedef typename Graph_traits::halfedge_descriptor halfedge_descriptor;
+  typedef typename Graph_traits::face_descriptor face_descriptor;
+  std::vector<vertex_descriptor> vertices;
   vertices.reserve(CH_2.size());
   BOOST_FOREACH(const Point_3& p, CH_2){
     vertices.push_back(add_vertex(P));
     put(vpm, vertices.back(),p);
   }
-  Euler::add_face(vertices, P);
+  face_descriptor f = Euler::add_face(vertices, P);
+
+  // Then triangulate that face
+  const halfedge_descriptor he = halfedge(f, P);
+  halfedge_descriptor other_he = next(next(he, P), P);
+  for(std::size_t i = 3, end = vertices.size(); i < end; ++i) {
+    const halfedge_descriptor next_he = next(other_he, P);
+    Euler::split_face(other_he, he, P);
+    other_he = next_he;
+  }
 }
 
 
diff --git a/Convex_hull_3/test/Convex_hull_3/quickhull_test_3.cpp b/Convex_hull_3/test/Convex_hull_3/quickhull_test_3.cpp
index c5c4f22a255..61756f28d79 100644
--- a/Convex_hull_3/test/Convex_hull_3/quickhull_test_3.cpp
+++ b/Convex_hull_3/test/Convex_hull_3/quickhull_test_3.cpp
@@ -106,6 +106,22 @@ void test_small_hull()
           polyhedron2.size_of_facets() == 6 );
 }
 
+void test_coplanar_hull()
+{
+  std::vector<Point_3> points;
+  points.push_back(Point_3(0,0,0));
+  points.push_back(Point_3(1,0,0));
+  points.push_back(Point_3(0,1,0));
+  points.push_back(Point_3(1,1,0));
+  points.push_back(Point_3(1.5,0.5,0));
+  points.push_back(Point_3(0.5,1.1,0));
+  Polyhedron_3 polyhedron;
+  CGAL::convex_hull_3(points.begin(), points.end(), polyhedron, Traits());
+  assert( polyhedron.is_valid() );
+  assert( polyhedron.size_of_facets() == 4 );
+  assert( polyhedron.is_pure_triangle() );
+}
+
 
 int main()
 {
@@ -115,6 +131,8 @@ int main()
   test_tetrahedron_convexity();
   std::cerr << "Testing small hull" << std::endl;
   test_small_hull();
+  std::cerr << "Testing coplanar hull" << std::endl;
+  test_coplanar_hull();
 
   std::cerr << "Testing 500 random points" << std::endl;
   std::vector<Point_3> points;