diff --git a/CHANGELOG.md b/CHANGELOG.md
index 19a37036..2d55a59d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -36,6 +36,7 @@ All notable changes to this project will be documented in this file.
 
 ### Fixed
 
+- #200: Keep the physical dimension of the mappings in `Domain.export` and `Domain.from_file`. The `topology.yml` metadata now stores `ldim` and `pdim` instead of `dim`, and `Domain.from_file` raises an error for files with the old `dim` key.
 - #140: Fix the rendering of the `Domain.join()` API documentation.
 - #166: Restore warning-free documentation builds, including bibliography and mathematical notation support.
 - #106: Preserve symbol assumptions and free-symbol information with modern SymPy.
diff --git a/sympde/topology/domain.py b/sympde/topology/domain.py
index 1a16f4f2..77271b8a 100644
--- a/sympde/topology/domain.py
+++ b/sympde/topology/domain.py
@@ -31,7 +31,6 @@
 # TODO fix circular dependency between domain and mapping
 if TYPE_CHECKING:
     from sympde.topology.mapping import Mapping
-# TODO add pdim
 
 iterable_types = (tuple, list, Tuple, Union)
 
@@ -336,7 +335,9 @@ def get_interior(self, name):
 
     def todict(self):
         name         = str(self.name)
-        dim          = str(self.dim)
+        ldim         = str(self.dim)
+        mappings     = [m for m in self.mappings.values() if m is not None]
+        pdim         = str(mappings[0].pdim) if mappings else ldim
         interior     = self.interior.todict()
         boundary     = self.boundary.todict()
         connectivity = self.connectivity.todict()
@@ -346,7 +347,8 @@ def todict(self):
             dtype = 'None'
 
         d = {'name':         name,
-             'dim':          dim,
+             'ldim':         ldim,
+             'pdim':         pdim,
              'dtype':        dtype,
              'interior':     interior,
              'boundary':     boundary,
@@ -404,8 +406,13 @@ def from_file(cls, filename):
         h5  = h5py.File( filename, mode='r' )
         yml = yaml.load( h5['topology.yml'][()], Loader=yaml.SafeLoader )
 
+        if 'dim' in yml:
+            raise ValueError(f"'{filename}' was written by an older version of SymPDE:"
+                             " replace its 'dim' key with the keys 'ldim' and 'pdim'")
+
         domain_name    = yml['name']
-        dim            = int(yml['dim'])
+        ldim           = int(yml['ldim'])
+        pdim           = int(yml['pdim'])
         dtype          = yml['dtype']
         d_interior     = yml['interior']
         d_boundary     = yml['boundary']
@@ -422,7 +429,7 @@ def from_file(cls, filename):
 
         constructors = [globals()[dt['type']] for dt in dtype]
         interiors    = [cs(i['name'], **dt['parameters']) for cs,i,dt in zip(constructors, d_interior, dtype)]
-        mappings     = [Mapping(I['mapping'], dim=dim) if I.get('mapping', "None") != "None" else None for I in d_interior]
+        mappings     = [Mapping(I['mapping'], ldim=ldim, pdim=pdim) if I.get('mapping', "None") != "None" else None for I in d_interior]
         domains      = [mapping(i) if mapping else i for i,mapping in zip(interiors, mappings)]
         patch_index  = {I.name:ind for ind,I in enumerate(interiors)}
 
diff --git a/sympde/topology/tests/test_topology.py b/sympde/topology/tests/test_topology.py
index 13002fa4..4c5546a5 100644
--- a/sympde/topology/tests/test_topology.py
+++ b/sympde/topology/tests/test_topology.py
@@ -1,5 +1,9 @@
 import os
 
+import h5py
+import numpy as np
+import pytest
+import yaml
 from sympy import preorder_traversal
 from sympy.core import Basic
 
@@ -113,6 +117,31 @@ def test_topology_1():
 
     assert D.todict() == Omega.todict()
 
+#==============================================================================
+def test_export_surface_mapping(tmp_path):
+    domain = Mapping('F', ldim=2, pdim=3)(Square('Omega'))
+
+    filename = str(tmp_path / 'surface.h5')
+    domain.export(filename)
+    D = Domain.from_file(filename)
+
+    assert D.mapping.ldim == 2
+    assert D.mapping.pdim == 3
+    assert D.todict() == domain.todict()
+
+#==============================================================================
+def test_from_file_with_old_dim_key(tmp_path):
+    yml = Mapping('F', dim=2)(Square('Omega')).todict()
+    yml['dim'] = yml.pop('ldim')
+    del yml['pdim']
+
+    filename = str(tmp_path / 'old.h5')
+    with h5py.File(filename, mode='w') as h5:
+        h5['topology.yml'] = np.array(yaml.dump(data=yml, sort_keys=None), dtype='S')
+
+    with pytest.raises(ValueError, match="older version of SymPDE"):
+        Domain.from_file(filename)
+
 #==============================================================================
 def test_domain_1():
     Omega_1 = InteriorDomain('Omega_1', dim=2)