diff --git a/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp
index 5c3d87bbb3a..3ebc983c9d4 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp
@@ -1204,14 +1204,28 @@ void Polyhedron_demo_cut_plugin::createCutPlane() {
     CGAL::Three::Scene_item* item = scene->item(i);
     Scene_polyhedron_item* poly_item = qobject_cast<Scene_polyhedron_item*>(item);
     if(!poly_item) continue;
-
+    if(!poly_item->polyhedron()->is_pure_triangle())
+    {
+      messages->warning(QString("%1 ignored (not a triangulated mesh)").arg(poly_item->name()));
+      continue;
+    }
     if(facet_trees.find(poly_item) == facet_trees.end()) {
       facet_trees[poly_item] = new Facet_tree();
       PPMAP pmap;
-      facet_trees[poly_item]->insert(faces(*(poly_item->polyhedron())).first,
-                                     faces(*(poly_item->polyhedron())).second,
-                                     *poly_item->polyhedron(),
-                                     pmap );
+      //filter facets to ignore degenerated ones
+      for(Polyhedron::Facet_iterator
+          fit = poly_item->polyhedron()->facets_begin(),
+          end = poly_item->polyhedron()->facets_end();
+          fit!=end; ++fit)
+      {
+        Polyhedron::Point a(fit->halfedge()->vertex()->point()),
+            b(fit->halfedge()->next()->vertex()->point()),
+            c(fit->halfedge()->prev()->vertex()->point());
+
+        if(!CGAL::collinear(a,b,c))
+          facet_trees[poly_item]->insert(Facet_primitive(fit, *poly_item->polyhedron(), pmap));
+      }
+
       Scene_aabb_item* aabb_item = new Scene_aabb_item(*facet_trees[poly_item]);
       aabb_item->setName(tr("AABB tree of %1").arg(poly_item->name()));
       aabb_item->setRenderingMode(Wireframe);