diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Plane_3_Plane_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Plane_3_Plane_3_intersection.h
index 2aa4e9b0bcb..2f4b6e75906 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Plane_3_Plane_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Plane_3_Plane_3_Plane_3_intersection.h
@@ -27,7 +27,7 @@ namespace internal {
 
 //  triple plane intersection
 template <class K>
-typename K::Point_3
+boost::optional<typename K::Point_3>
 intersection_point(const typename K::Plane_3& plane1,
                    const typename K::Plane_3& plane2,
                    const typename K::Plane_3& plane3,
@@ -55,6 +55,10 @@ intersection_point(const typename K::Plane_3& plane1,
 
   const FT den = minor_0*m22 - minor_1*m12 + minor_2*m02; // determinant of M
 
+  if(is_zero(den)){
+    return boost::none;
+  }
+
   const FT num3 = minor_0*b2 - minor_1*b1 + minor_2*b0;  // determinant of M with M[x:2] swapped with [b0,b1,b2]
 
   // Minors common to two determinants
@@ -66,7 +70,7 @@ intersection_point(const typename K::Plane_3& plane1,
   const FT num1 = - minor_3*m21 + minor_4*m11 - minor_5*m01;  // determinant of M with M[x:0] swapped with [b0,b1,b2]
   const FT num2 = minor_3*m20 - minor_4*m10 + minor_5*m00;  // determinant of M with M[x:1] swapped with [b0,b1,b2]
 
-  return typename K::Point_3(num1/den, num2/den, num3/den);
+  return boost::make_optional(typename K::Point_3(num1/den, num2/den, num3/den));
 }
 
 template <class K>
@@ -83,12 +87,9 @@ intersection(const typename K::Plane_3& plane1,
   typedef typename K::Line_3       Line_3;
   typedef typename K::Plane_3      Plane_3;
 
-  if(!is_zero(determinant(plane1.a(), plane1.b(), plane1.c(),
-                          plane2.a(), plane2.b(), plane2.c(),
-                          plane3.a(), plane3.b(), plane3.c())))
-  {
-    return result_type(intersection_point(plane1,plane2,plane3, k));
-  }
+  auto res = intersection_point(plane1,plane2,plane3, k);
+  if (res != boost::none)
+    return result_type(*res);
 
   // Intersection between plane1 and plane2 can either be
   // a line, a plane, or empty.