diff --git a/Polyhedron/include/CGAL/Polyhedron_3.h b/Polyhedron/include/CGAL/Polyhedron_3.h
index 278d3b9b8a2..922c5110e69 100644
--- a/Polyhedron/include/CGAL/Polyhedron_3.h
+++ b/Polyhedron/include/CGAL/Polyhedron_3.h
@@ -111,7 +111,8 @@ public:
 
     // the degree of the vertex, i.e., edges emanating from this vertex
     std::size_t vertex_degree() const {
-        return this->halfedge()->vertex_degree();
+        return this->halfedge()!=Halfedge_const_handle()
+               ? this->halfedge()->vertex_degree() : 0;
     }
     size_type degree() const { return vertex_degree(); } //backwards compatible