diff --git a/openmc/cell.py b/openmc/cell.py
index ba7a41435..522f9ab5d 100644
--- a/openmc/cell.py
+++ b/openmc/cell.py
@@ -1,4 +1,5 @@
 from collections import OrderedDict, Iterable
+from copy import deepcopy
 from math import cos, sin, pi
 from numbers import Real, Integral
 from xml.etree import ElementTree as ET
@@ -508,7 +509,7 @@ class Cell(object):
         """Create a copy of this cell with a new unique ID, and clones
         the cell's region and fill."""
 
-        clone = copy.deepcopy(self)
+        clone = deepcopy(self)
         clone.id = None
 
         if self.region is not None:
diff --git a/openmc/lattice.py b/openmc/lattice.py
index 9f3f30385..b98ef0087 100644
--- a/openmc/lattice.py
+++ b/openmc/lattice.py
@@ -2,6 +2,7 @@ from __future__ import division
 
 from abc import ABCMeta
 from collections import OrderedDict, Iterable
+from copy import deepcopy
 from math import sqrt, floor
 from numbers import Real, Integral
 from xml.etree import ElementTree as ET
@@ -418,7 +419,7 @@ class Lattice(object):
         """Create a copy of this lattice with a new unique ID, and clones
         all universes within this lattice."""
 
-        clone = copy.deepcopy(self)
+        clone = deepcopy(self)
         clone.id = None
 
         # Clone all unique universes in the lattice
@@ -427,9 +428,17 @@ class Lattice(object):
             univ_clones[univ_id] = univ_clones[univ_id].clone()
 
         # Assign universe clones to the lattice clone
-        for index in self.indices:
-            univ_id = self.universe[index].id
-            clone.universes[index] = univ_clones[univ_id]
+        for i in self.indices:
+            if isinstance(self, RectLattice):
+                univ_id = self.universes[i].id
+                clone.universes[i] = univ_clones[univ_id]
+            else:
+                if self.ndim == 2:
+                    univ_id = self.universes[i[0]][i[1]].id
+                    clone.universes[i[0]][i[1]] = univ_clones[univ_id]
+                else:
+                    univ_id = self.universes[i[0]][i[1]][i[2]].id
+                    clone.universes[i[0]][i[1]][i[2]] = univ_clones[univ_id]
 
         return clone
 
diff --git a/openmc/material.py b/openmc/material.py
index cb1482b8e..be13d619f 100644
--- a/openmc/material.py
+++ b/openmc/material.py
@@ -799,6 +799,13 @@ class Material(object):
 
         return nuclides
 
+    def clone(self):
+        """Create a copy of this material with a new unique ID."""
+
+        clone = deepcopy(self)
+        clone.id = None
+        return clone
+
     def _get_nuclide_xml(self, nuclide, distrib=False):
         xml_element = ET.Element("nuclide")
         xml_element.set("name", nuclide[0].name)
@@ -1100,13 +1107,6 @@ class Materials(cv.CheckedList):
         for material in self:
             material.make_isotropic_in_lab()
 
-    def clone(self):
-        """Create a copy of this material with a new unique ID."""
-
-        clone = copy.deepcopy(self)
-        clone.id = None
-        return clone
-
     def _create_material_subelements(self, root_element):
         for material in self:
             root_element.append(material.to_xml_element(self.cross_sections))
diff --git a/openmc/region.py b/openmc/region.py
index 1ac4d8c94..b93d305fe 100644
--- a/openmc/region.py
+++ b/openmc/region.py
@@ -1,5 +1,6 @@
 from abc import ABCMeta, abstractmethod
 from collections import Iterable, OrderedDict
+from copy import deepcopy
 
 from six import add_metaclass
 import numpy as np
@@ -306,12 +307,11 @@ class Intersection(Region):
         check_type('nodes', nodes, Iterable, Region)
         self._nodes = nodes
 
-    @abstractmethod
     def clone(self):
         """Create a copy of this region - each of the surfaces in the
         intersection's nodes will be cloned and will have new unique IDs."""
 
-        clone = copy.deepcopy(self)
+        clone = deepcopy(self)
         clone.nodes = [n.clone() for n in self.nodes]
         return clone
 
diff --git a/openmc/surface.py b/openmc/surface.py
index b0aa250c0..866a9e2b9 100644
--- a/openmc/surface.py
+++ b/openmc/surface.py
@@ -1,5 +1,6 @@
 from abc import ABCMeta
 from collections import Iterable, OrderedDict
+from copy import deepcopy
 from numbers import Real, Integral
 from xml.etree import ElementTree as ET
 from math import sqrt
@@ -174,7 +175,7 @@ class Surface(object):
     def clone(self):
         """Create a copy of this surface with a new unique ID."""
 
-        clone = copy.deepcopy(self)
+        clone = deepcopy(self)
         clone.id = None
         return clone
 
@@ -1828,15 +1829,6 @@ class Halfspace(Region):
     def __init__(self, surface, side):
         self.surface = surface
         self.side = side
-
-    @abstractmethod
-    def clone(self):
-        """Create a copy of this halfspace, with a cloned surface with a
-        unique ID."""
-
-        clone = copy.deepcopy(self)
-        clone.surface = self.surface.clone()
-        return clone
         
     def __and__(self, other):
         if isinstance(other, Intersection):
@@ -1918,6 +1910,14 @@ class Halfspace(Region):
         surfaces[self.surface.id] = self.surface
         return surfaces
 
+    def clone(self):
+        """Create a copy of this halfspace, with a cloned surface with a
+        unique ID."""
+
+        clone = deepcopy(self)
+        clone.surface = self.surface.clone()
+        return clone
+
 
 def get_rectangular_prism(width, height, axis='z', origin=(0., 0.),
                           boundary_type='transmission'):
diff --git a/openmc/universe.py b/openmc/universe.py
index 0f5e2da14..a2157f1d7 100644
--- a/openmc/universe.py
+++ b/openmc/universe.py
@@ -1,6 +1,6 @@
 from __future__ import division
-from copy import copy
 from collections import OrderedDict, Iterable
+from copy import copy, deepcopy
 from numbers import Integral, Real
 import random
 import sys
@@ -521,7 +521,7 @@ class Universe(object):
         """Create a copy of this universe with a new unique ID, and clones
         all cells within this universe."""
 
-        clone = copy.deepcopy(self)
+        clone = deepcopy(self)
         clone.id = None
 
         # Clone all cells for the universe clone