diff --git a/blender/samples/cube-no-connectivity.json b/blender/samples/cube-no-connectivity.json
new file mode 100644
index 0000000..0e0578b
--- /dev/null
+++ b/blender/samples/cube-no-connectivity.json
@@ -0,0 +1 @@
+{"edges": [[4, 5], [5, 1], [1, 0], [0, 4], [5, 6], [6, 2], [2, 1], [6, 7], [7, 3], [3, 2], [7, 4], [0, 3]], "vertices": [[-1.0, -1.0, -1.0], [-1.0, 1.0, -1.0], [1.0, 1.0, -1.0], [1.0, -1.0, -1.0], [-1.0, -1.0, 1.0], [-1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, -1.0, 1.0]], "faces": [[4, 5, 1, 0], [5, 6, 2, 1], [6, 7, 3, 2], [7, 4, 0, 3], [0, 1, 2, 3], [7, 6, 5, 4]]}
diff --git a/surf/geometry.py b/surf/geometry.py
index 88ab767..c2a3e67 100644
--- a/surf/geometry.py
+++ b/surf/geometry.py
@@ -207,6 +207,8 @@ class PolygonMesh(object):
             'vertices': self.vertices,
             'edges': self.edges,
             'faces': self.faces,
+            'faces_for_vert': self.faces_for_vert,
+            'edges_for_vert': self.edges_for_vert,
         }
         return json.dumps(d)
 
diff --git a/surf/test/test_polymesh.py b/surf/test/test_polymesh.py
index e7500f8..6e3d277 100644
--- a/surf/test/test_polymesh.py
+++ b/surf/test/test_polymesh.py
@@ -11,17 +11,38 @@ class TestPM(unittest.TestCase):
         path, file_name = os.path.split(__file__)
         self.samples_dir = os.path.join(path, os.pardir, os.pardir,
                 'blender', 'samples')
-        cube_file_name = os.path.join(self.samples_dir, 'cube.json')
+        full_cube_file_name = os.path.join(self.samples_dir, 'cube.json')
+        with open(full_cube_file_name) as cube_file:
+            self.full_cube = json.load(cube_file)
+
+        cube_file_name = os.path.join(self.samples_dir, 'cube-no-connectivity.json')
         with open(cube_file_name) as cube_file:
-            self.cube = json.load(cube_file)
+            self.skeleton_cube = json.load(cube_file)
+
+        self.skel = PolygonMesh(**self.skeleton_cube)
+        self.cube = PolygonMesh(**self.full_cube)
 
     def test_cube_load(self):
-        p = PolygonMesh(**self.cube)
+        p = PolygonMesh(**self.full_cube)
         v = p.vertices[0]
         self.assertAlmostEqual(v.x, -1.0)
         self.assertAlmostEqual(v.y, -1.0)
         self.assertAlmostEqual(v.z, -1.0)
 
+    def test_connectivity(self):
+        self.skel.faces_for_vert
+        self.skel.edges_for_vert
+        self.skel.edges_for_face
+        self.skel.faces_for_edge
+
+    def test_faces_for_vert(self):
+        for pi, qi in zip(self.skel.faces_for_vert, self.cube.faces_for_vert):
+            self.assertEqual(sorted(pi), sorted(qi))
+
+    def test_edges_for_vert(self):
+        for pi, qi in zip(self.skel.edges_for_vert, self.cube.edges_for_vert):
+            self.assertEqual(sorted(pi), sorted(qi))
+
 
 if __name__ == '__main__':
     unittest.main(verbosity=3)