diff --git a/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
index a0987b3529f..f5ee6802f7a 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
@@ -27,6 +27,7 @@
 #define CGAL_TRIANGLE_3_TETRAHEDRON_3_DO_INTERSECT_H
 
 #include <CGAL/Triangle_3_Triangle_3_do_intersect.h>
+#include <CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h>
 
 namespace CGAL {
 
@@ -36,11 +37,12 @@ namespace CGAL {
 namespace internal {
 
 // This code is not optimized:
-template <class K>
+  template <class K, class Bounded>
 typename K::Boolean
-do_intersect(const typename K::Triangle_3 &tr,
-             const typename K::Tetrahedron_3 &tet,
-             const K & k)
+do_intersect_tetrahedron_bounded(const typename Bounded &tr,
+                                 const typename K::Tetrahedron_3 &tet,
+                                 const typename K::Point_3 p,
+                                 const K & k)
 {
     typedef typename K::Triangle_3 Triangle;
 
@@ -52,12 +54,7 @@ do_intersect(const typename K::Triangle_3 &tr,
     if (do_intersect(tr, Triangle(tet[0], tet[2], tet[3]), k)) return true;
     if (do_intersect(tr, Triangle(tet[1], tet[2], tet[3]), k)) return true;
 
-    CGAL_kernel_assertion(k.bounded_side_3_object()(tet, tr[0]) ==
-                          k.bounded_side_3_object()(tet, tr[1]));
-    CGAL_kernel_assertion(k.bounded_side_3_object()(tet, tr[0]) ==
-                          k.bounded_side_3_object()(tet, tr[2]));
-
-    return k.has_on_bounded_side_3_object()(tet, tr[0]);
+    return k.has_on_bounded_side_3_object()(tet, p);
 }
 
 
@@ -68,12 +65,134 @@ do_intersect(const typename K::Tetrahedron_3 &tet,
 	     const typename K::Triangle_3 &tr,
 	     const K & k)
 {
-  return do_intersect(tr, tet, k);
+  return do_intersect_tetrahedron_bounded(tr, tet, tr[0], k);
 }
 
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Triangle_3 &tr,
+             const typename K::Tetrahedron_3 &tet,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(tr, tet, tr[0], k);
+}
+
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Tetrahedron_3 &tet,
+	     const typename K::Segment_3 &seg,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(seg, tet, seg.source(), k);
+}
+    
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Segment_3 &seg,
+             const typename K::Tetrahedron_3 &tet,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(seg, tet, seg.source(), k);
+}
+  
+
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Tetrahedron_3 &tet,
+             const typename K::Iso_cuboid_3 &ic,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(ic, tet, ic[0], k);
+}
+
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Iso_cuboid_3 &ic,
+             const typename K::Tetrahedron_3 &tet,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(ic, tet, ic[0], k);
+}
+
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Tetrahedron_3 &tet,
+             const typename K::Sphere_3 &sp,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(sp, tet, sp.center(), k);
+}
+
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Sphere_3 &sp,
+             const typename K::Tetrahedron_3 &tet,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(sp, tet, sp.center(), k);
+}
+
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Tetrahedron_3 &tet,
+	     const typename K::Tetrahedron_3 &sp,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(sp, tet, tet[0], k);
+}
+
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Tetrahedron_3 &tet,
+	     const typename Bbox_3 &bb,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(bb, tet, typename K::Point_3(bb.xmin(), bb.ymin(), bb.zmin()), k);
+}
+
+  template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename Bbox_3 &bb,
+             const typename K::Tetrahedron_3 &tet,
+	     const K & k)
+{
+  return do_intersect_tetrahedron_bounded(bb, tet, typename K::Point_3(bb.xmin(), bb.ymin(), bb.zmin()), k);
+}
+  
 } // namespace internal
 
 CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Tetrahedron_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Segment_3, Tetrahedron_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Iso_cuboid_3, Tetrahedron_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Sphere_3, Tetrahedron_3, 3)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Tetrahedron_3, 3)
+
+
+template<typename K>
+bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+  
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3& b,
+                  const CGAL::Tetrahedron_3<K>& a) {
+  return K().do_intersect_3_object()(a, b);
+}
 
 } //namespace CGAL
 
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h
new file mode 100644
index 00000000000..b735b3d2346
--- /dev/null
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h
@@ -0,0 +1,116 @@
+// Copyright (c) 2018  GeometryFactory Sarl (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0+
+//
+//
+// Author(s)     : Andreas Fabri
+
+#ifndef CGAL_INTERNAL_INTERSECTIONS_3_TETRAHEDRON_3_DO_INTERSECT_H
+#define CGAL_INTERNAL_INTERSECTIONS_3_TETRAHEDRON_3_DO_INTERSECT_H
+
+#include <CGAL/Tetrahedron_3.h>
+#include <CGAL/Plane_3.h>
+#include <CGAL/Line_3.h>
+#include <CGAL/Ray_3.h>
+
+namespace CGAL {
+
+namespace internal {
+
+template<typename K, class Unbounded>
+bool do_intersect_tetrahedron_unbounded(const typename K::Tetrahedron_3& tet,
+                                        const Unbounded& unb,
+                                        const K& k) {
+    if (do_intersect(unb, Triangle(tet[0], tet[1], tet[2]), k)) return true;
+    if (do_intersect(unb, Triangle(tet[0], tet[1], tet[3]), k)) return true;
+    if (do_intersect(unb, Triangle(tet[0], tet[2], tet[3]), k)) return true;
+    if (do_intersect(unb, Triangle(tet[1], tet[2], tet[3]), k)) return true;
+    return false;
+}
+
+
+
+template<typename K>
+bool do_intersect(const typename K::Tetrahedron_3& tet,
+                  const typename K::Plane_3& unb,
+                  const K& k) {
+  return do_intersect_tetrahedron_unbounded(tet, unb, k);
+}
+
+
+template<typename K>
+bool do_intersect(const typename K::Tetrahedron_3& tet,
+                  const typename K::Line_3& unb,
+                  const K& k) {
+  return do_intersect_tetrahedron_unbounded(tet, unb, k);
+}
+
+
+template<typename K>
+bool do_intersect(const typename K::Tetrahedron_3& tet,
+                  const typename K::Ray_3& unb,
+                  const K& k) {
+  return do_intersect_tetrahedron_unbounded(tet, unb, k);
+}
+  
+} // namespace internal
+
+    
+template<typename K>
+bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
+                  const CGAL::Plane_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+  
+template<typename K>
+bool do_intersect(const CGAL::Plane_3<K>& b,
+                  const CGAL::Tetrahedron_3<K>& a) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+  
+template<typename K>
+bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
+                  const CGAL::Line_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+  
+template<typename K>
+bool do_intersect(const CGAL::Line_3<K>& b,
+                  const CGAL::Tetrahedron_3<K>& a) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+  
+template<typename K>
+bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
+                  const CGAL::Ray_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+  
+template<typename K>
+bool do_intersect(const CGAL::Ray_3<K>& b,
+                  const CGAL::Tetrahedron_3<K>& a) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+} // namespace CGAL
+
+#endif CGAL_INTERNAL_INTERSECTIONS_3_TETRAHEDRON_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h
new file mode 100644
index 00000000000..8c129fa07a4
--- /dev/null
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h
@@ -0,0 +1,125 @@
+// Copyright (c) 2018 GeometryFactory Sarl  
+// All rights reserved. 
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0+
+// 
+//
+// Author(s)     : Andreas Fabri
+
+#ifndef CGAL_TRIANGLE_3_SPHERE_3_DO_INTERSECT_H
+#define CGAL_TRIANGLE_3_SPHERE_3_DO_INTERSECT_H
+
+#include <CGAL/squared_distance_3_2.h>
+#include <CGAL/Intersection_traits_3.h>
+
+namespace CGAL {
+
+  template <class K>
+  class Triangle_3;
+  
+  template <class K>
+  class Sphere_3;
+
+  template <class K>
+  class Line_3;
+  
+namespace internal {
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Sphere_3 &sp,
+             const typename K::Triangle_3 &tr,
+	     const K & k)
+{
+  return squared_distance(sp.center(), tr) <= sp.squared_radius();
+}
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Sphere_3 &sp,
+             const typename K::Line_3 &lin,
+	     const K & k)
+{
+  return squared_distance(sp.center(), lin) <= sp.squared_radius();
+}
+
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Line_3 &lin,
+	     const typename K::Sphere_3 &sp,
+	     const K & k)
+{
+  return squared_distance(sp.center(), lin) <= sp.squared_radius();
+}
+
+
+
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Sphere_3 &sp,
+             const typename K::Ray_3 &lin,
+	     const K & k)
+{
+  return squared_distance(sp.center(), lin) <= sp.squared_radius();
+}
+
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Ray_3 &lin,
+	     const typename K::Sphere_3 &sp,
+	     const K & k)
+{
+  return squared_distance(sp.center(), lin) <= sp.squared_radius();
+}
+
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Sphere_3 &sp,
+             const typename K::Segment_3 &lin,
+	     const K & k)
+{
+  return squared_distance(sp.center(), lin) <= sp.squared_radius();
+}
+
+  
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Segment_3 &lin,
+	     const typename K::Sphere_3 &sp,
+	     const K & k)
+{
+  return squared_distance(sp.center(), lin) <= sp.squared_radius();
+}
+} // namespace internal
+
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Sphere_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Line_3, Sphere_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Ray_3, Sphere_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Segment_3, Sphere_3, 3)
+
+} // namespace CGAL
+
+#endif CGAL_TRIANGLE_3_SPHERE_3_DO_INTERSECT_H
+
diff --git a/Intersections_3/include/CGAL/intersection_3.h b/Intersections_3/include/CGAL/intersection_3.h
index f2cefb8f31c..3d74dbf38d4 100644
--- a/Intersections_3/include/CGAL/intersection_3.h
+++ b/Intersections_3/include/CGAL/intersection_3.h
@@ -64,6 +64,8 @@
 #include <CGAL/internal/Intersections_3/Iso_cuboid_3_Ray_3_do_intersect.h>
 #include <CGAL/internal/Intersections_3/Iso_cuboid_3_Sphere_3_do_intersect.h>
 #include <CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h>
+#include <CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h>
+#include <CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h>
 
 #include <CGAL/enable_warnings.h>
 
diff --git a/Intersections_3/test/Intersections_3/tetrahedron.cpp b/Intersections_3/test/Intersections_3/tetrahedron.cpp
new file mode 100644
index 00000000000..6c05a321df6
--- /dev/null
+++ b/Intersections_3/test/Intersections_3/tetrahedron.cpp
@@ -0,0 +1,56 @@
+#include <cassert>
+
+#include <CGAL/Cartesian.h>
+#include <CGAL/intersections.h>
+
+typedef CGAL::Cartesian<double> K;
+
+typedef K::Tetrahedron_3   Tetrahedron;
+
+typedef K::Segment_3       Segment;
+typedef K::Triangle_3      Triangle;
+typedef K::Iso_cuboid_3    Iso_cuboid;
+typedef K::Sphere_3        Sphere;
+
+typedef K::Plane_3         Plane;
+typedef K::Line_3          Line;
+typedef K::Ray_3           Ray;
+
+typedef CGAL::Bbox_3       Bbox;
+
+int main()
+{
+  Tetrahedron tet;
+  Sphere sp;
+  
+  CGAL::do_intersect(tet,Triangle());
+  CGAL::do_intersect(tet,Segment());
+  CGAL::do_intersect(tet,Iso_cuboid());
+  CGAL::do_intersect(tet,Sphere());
+  CGAL::do_intersect(tet,Plane());
+  CGAL::do_intersect(tet,Line());
+  CGAL::do_intersect(tet,Ray());  
+  CGAL::do_intersect(tet,tet);
+  CGAL::do_intersect(tet,Bbox());
+  CGAL::do_intersect(sp, Line());
+  CGAL::do_intersect(sp, Ray());
+  CGAL::do_intersect(sp, Segment());
+  
+  
+  CGAL::do_intersect(Triangle(), tet);
+  CGAL::do_intersect(Segment(), tet);
+  CGAL::do_intersect(Iso_cuboid(), tet);
+  CGAL::do_intersect(Sphere(), tet);
+  CGAL::do_intersect(Plane(), tet);
+  CGAL::do_intersect(Line(), tet);
+  CGAL::do_intersect(Ray(), tet);  
+  CGAL::do_intersect(Bbox(), tet);
+  
+  CGAL::do_intersect(Line(), sp);
+  CGAL::do_intersect(Ray(), sp);
+  CGAL::do_intersect(Segment(), sp);
+
+
+  return 0;
+  
+}
diff --git a/Intersections_3/test/Intersections_3/triangle_other.cpp b/Intersections_3/test/Intersections_3/triangle_other.cpp
index fdfccc372fe..d96a444b24b 100644
--- a/Intersections_3/test/Intersections_3/triangle_other.cpp
+++ b/Intersections_3/test/Intersections_3/triangle_other.cpp
@@ -1,7 +1,5 @@
 #include <cassert>
 
-
-#include <CGAL/basic.h>
 #include <CGAL/Cartesian.h>
 #include <CGAL/Triangle_2_Triangle_2_do_intersect.h>
 #include <CGAL/Triangle_3_Line_3_do_intersect.h>