diff --git a/apps/fan/src/common_refinement.cc b/apps/fan/src/common_refinement.cc
index 1e4a130..d436991 100644
--- a/apps/fan/src/common_refinement.cc
+++ b/apps/fan/src/common_refinement.cc
@@ -24,6 +24,30 @@
 
 namespace polymake { namespace fan {
 
+template<typename Coord>
+Array<perl::Object> construct_cones(const Array<Set<int> > & max_cones, const Matrix<Coord> & rays, const Matrix<Coord> & lin_space){
+   perl::ObjectType cone_type=perl::ObjectType::construct<Coord>("Cone");
+
+   int size = lin_space.rows() > 0 ? max_cones.size()+1 : max_cones.size();
+
+   Array<perl::Object> all_cones(size);
+   for (int i=0; i<max_cones.size(); ++i) {
+      all_cones[i].create_new(cone_type);
+      const Matrix<Coord> cone_vert=rays.minor(max_cones[i],All);
+      all_cones[i].take("RAYS")<<cone_vert;
+      all_cones[i].take("LINEALITY_SPACE")<<lin_space;
+   }
+
+   // if the fan does not have maximal cones, we still need something to intersect with
+   if (lin_space.rows() > 0) {
+      all_cones[max_cones.size()].create_new(cone_type);
+      const Matrix<Coord> ns = null_space(lin_space);
+      all_cones[max_cones.size()].take("INEQUALITIES")<< ns/(-ns);
+   }
+
+   return all_cones;
+}
+
 template <typename Coord>
 perl::Object common_refinement(perl::Object f1, perl::Object f2)
 {
@@ -32,8 +56,8 @@ perl::Object common_refinement(perl::Object f1, perl::Object f2)
    Matrix<Coord> rays1=f1.give("RAYS");
    const Matrix<Coord> lineality_space1=f1.give("LINEALITY_SPACE");
    const Matrix<Coord> lineality_space2=f2.give("LINEALITY_SPACE");
-   const Matrix<Coord> lineality_space =
-      null_space(null_space(lineality_space1) / null_space(lineality_space2));
+   const Matrix<Coord> lineality_space = (lineality_space1.cols() > 0 && lineality_space2.cols() > 0)?
+      null_space(null_space(lineality_space1) / null_space(lineality_space2)) : Matrix<Coord>() ;
    const Array<Set<int> > max_cones2=f2.give("MAXIMAL_CONES");
    Matrix<Coord> rays2=f2.give("RAYS");
    const bool complete = f1.give("COMPLETE") && f2.give("COMPLETE");
@@ -57,22 +81,8 @@ perl::Object common_refinement(perl::Object f1, perl::Object f2)
    }
    */
    std::list<Set<int> > new_max_cones;
-   perl::ObjectType cone_type=perl::ObjectType::construct<Coord>("Cone");
-
-   Array<perl::Object> all_cones1(max_cones1.size());
-   for (int i=0; i<max_cones1.size(); ++i) {
-      all_cones1[i].create_new(cone_type);
-      const Matrix<Coord> p1_cone_vert=rays1.minor(max_cones1[i],All);
-      all_cones1[i].take("RAYS")<<p1_cone_vert;
-      all_cones1[i].take("LINEALITY_SPACE")<<lineality_space1;
-   }
-   Array<perl::Object> all_cones2(max_cones2.size());
-   for (int i=0; i<max_cones2.size(); ++i) {
-      all_cones2[i].create_new(cone_type);
-      const Matrix<Coord> p2_cone_vert=rays2.minor(max_cones2[i],All);
-      all_cones2[i].take("RAYS")<<p2_cone_vert;
-      all_cones2[i].take("LINEALITY_SPACE")<<lineality_space2;
-   }
+   Array<perl::Object> all_cones1 = construct_cones(max_cones1, rays1, lineality_space1);
+   Array<perl::Object> all_cones2 = construct_cones(max_cones2, rays2, lineality_space2);
 
    for (Entire<Array<perl::Object> >::iterator i1=entire(all_cones1); !i1.at_end(); ++i1) {
       for (Entire<Array<perl::Object> >::iterator i2=entire(all_cones2); !i2.at_end(); ++i2) {
@@ -98,7 +108,7 @@ perl::Object common_refinement(perl::Object f1, perl::Object f2)
             Set<int> new_cone;
             for (Entire<sequence>::const_iterator j=entire(sequence(0,index)); !j.at_end(); ++j)
                if (ray_indices[*j]>=0) new_cone.insert(ray_indices[*j]);
-            new_max_cones.push_back(new_cone);
+            if (new_cone.size() > 0) new_max_cones.push_back(new_cone);
          }
       }
    }