diff --git a/rmgpy/molecule/molecule.py b/rmgpy/molecule/molecule.py
index a5d54a11d3..1d4f4752e4 100644
--- a/rmgpy/molecule/molecule.py
+++ b/rmgpy/molecule/molecule.py
@@ -2681,13 +2681,21 @@ def get_smallest_set_of_smallest_rings(self, symmetrized=False):
                                       return_mapping=False,
                                       save_order=True,
                                       ignore_bond_orders=True)
-
+        rdkit_mol.UpdatePropertyCache(strict=False)
+        ranks = list(Chem.CanonicalRankAtoms(rdkit_mol, breakTies=True))
+        rank_to_idx = {rank: idx for idx, rank in enumerate(ranks)}
+        new_order = [rank_to_idx[i] for i in range(rdkit_mol.GetNumAtoms())]
+        canonical_mol = Chem.RenumberAtoms(rdkit_mol, new_order)
         if symmetrized:
-            ring_info = Chem.GetSymmSSSR(rdkit_mol)
+            ring_info = Chem.GetSymmSSSR(canonical_mol)
         else:
-            ring_info = Chem.GetSSSR(rdkit_mol)
+            ring_info = Chem.GetSSSR(canonical_mol)
+
         for ring in ring_info:
-            atom_ring = [self.atoms[idx] for idx in ring]
+            # Map the new canonical indices back to the original RMG atom indices
+            original_idx_ring = [new_order[idx] for idx in ring]
+            atom_ring = [self.atoms[idx] for idx in original_idx_ring]
+            
             sorted_ring = self.sort_cyclic_vertices(atom_ring)
             sssr.append(sorted_ring)
         if symmetrized:
diff --git a/test/rmgpy/molecule/moleculeTest.py b/test/rmgpy/molecule/moleculeTest.py
index 43c4b4e33a..2c3896148d 100644
--- a/test/rmgpy/molecule/moleculeTest.py
+++ b/test/rmgpy/molecule/moleculeTest.py
@@ -3172,8 +3172,8 @@ def test_get_all_polycyclic_vertices(self):
         """)
         polycyclic_vertices = mol.get_all_polycyclic_vertices()
         assert len(polycyclic_vertices) == 2
-        assert mol.atoms[0] is mol.get_all_polycyclic_vertices()[0]
-        assert mol.atoms[1] is mol.get_all_polycyclic_vertices()[1]
+        assert mol.atoms[0] is mol.get_all_polycyclic_vertices()[1]
+        assert mol.atoms[1] is mol.get_all_polycyclic_vertices()[0]
         
         # Spirocyclic molecule
         mol = Molecule().from_adjacency_list("""