diff --git a/surf/subd/butterfly.py b/surf/subd/butterfly.py
index 18e382a..92f3b96 100644
--- a/surf/subd/butterfly.py
+++ b/surf/subd/butterfly.py
@@ -1,5 +1,7 @@
 from __future__ import division
 
+from itertools import combinations
+
 from surf.geometry import PolygonMesh, Vertex
 
 
@@ -57,4 +59,10 @@ def refine(mesh):
             new_edge = [evid, new_vert_id]
             new_edges.append(new_edge)
 
+    for fid in range(len(mesh.faces)):
+        # join all new edge points on a face:
+        new_edges.extend(
+                [[i[0] + nv_offset, i[1] + nv_offset]
+                    for i in combinations(mesh.edges_for_face[fid], 2)])
+
     return PolygonMesh(new_verts, new_faces, new_edges)