diff --git a/xugrid/conversion.py b/xugrid/conversion.py
index ee42cdda..d6540373 100644
--- a/xugrid/conversion.py
+++ b/xugrid/conversion.py
@@ -283,23 +283,32 @@ def bounds1d_to_vertices(bounds: np.ndarray):
 def bounds2d_to_vertices(
     x_bounds: np.ndarray, y_bounds: np.ndarray
 ) -> Tuple[FloatArray, BoolArray]:
-    # Create 2D coords, discard NaNs.
+    x = x_bounds.reshape(-1, 4)
+    y = y_bounds.reshape(-1, 4)
+    # Make sure repeated nodes are consecutive so we can find them later.
+    # lexsort along axis 1.
+    sorter = np.lexsort((y, x))
     face_node_coordinates = np.stack(
         (
-            x_bounds.reshape(-1, 4),
-            y_bounds.reshape(-1, 4),
+            np.take_along_axis(x, sorter, axis=1),
+            np.take_along_axis(y, sorter, axis=1),
         ),
         axis=-1,
     )
     index = np.isfinite(face_node_coordinates.reshape(-1, 8)).all(axis=-1)
     face_node_coordinates = face_node_coordinates[index]
 
-    # Guarantee counterclockwise orientation
+    # Guarantee counterclockwise orientation.
     face_centroids = np.mean(face_node_coordinates, axis=1)
     dx = face_node_coordinates[..., 0] - face_centroids[:, np.newaxis, 0]
     dy = face_node_coordinates[..., 1] - face_centroids[:, np.newaxis, 1]
     angle = np.arctan2(dy, dx)
+    # When nodes are repeated, make sure the repeated node ends up as last so we can
+    # construct the face_node_connectivity directly from it. We do so by inserting
+    # an angle of np.inf for the repeated nodes.
+    angle[:, 1:][angle[:, 1:] == angle[:, :-1]] = np.inf
     counterclockwise = np.argsort(angle, axis=1)
+
     face_node_coordinates = np.take_along_axis(
         face_node_coordinates, counterclockwise[..., None], axis=1
     )
diff --git a/xugrid/ugrid/ugrid2d.py b/xugrid/ugrid/ugrid2d.py
index 6691d88f..bf2b586a 100644
--- a/xugrid/ugrid/ugrid2d.py
+++ b/xugrid/ugrid/ugrid2d.py
@@ -2251,10 +2251,29 @@ def from_structured_bounds(
             xy, inverse = np.unique(
                 face_node_coordinates.reshape((-1, 2)), return_inverse=True, axis=0
             )
+            face_node_connectivity = inverse.reshape((-1, 4))
+
+            # Check whether all coordinates form valid UGRID topologies.
+            # We can only maintain triangles and quadrangles.
+            valid = face_node_connectivity != np.roll(face_node_connectivity, 1, axis=1)
+            if not valid.all():
+                xy = xy[np.unique(face_node_connectivity[valid])]
+                keep = valid.sum(axis=1) >= 3
+                warnings.warn(
+                    "A UGRID2D face requires at least three unique vertices.\n"
+                    f"Your structured bounds contain {len(keep) - keep.sum()} invalid faces.\n"
+                    "These will be omitted from the Ugrid2d topology.",
+                )
+                index = index[keep]
+                face_node_connectivity[~valid] = -1
+                face_node_connectivity = connectivity.renumber(
+                    face_node_connectivity[keep]
+                )
+
             grid = Ugrid2d(
                 *xy.T,
                 -1,
-                face_node_connectivity=inverse.reshape((-1, 4)),
+                face_node_connectivity=face_node_connectivity,
                 name=name,
             )
         else: