diff --git a/openmc/lattice.py b/openmc/lattice.py
index 3bb6e825e1..be5f22db93 100644
--- a/openmc/lattice.py
+++ b/openmc/lattice.py
@@ -56,11 +56,11 @@ class Lattice(object):
             return False
         elif self.name != other.name:
             return False
-        elif self.pitch != other.pitch:
+        elif np.any(self.pitch != other.pitch):
             return False
         elif self.outer != other.outer:
             return False
-        elif self.universes != other.universes:
+        elif np.any(self.universes != other.universes):
             return False
         else:
             return True
@@ -533,7 +533,7 @@ class RectLattice(Lattice):
             return False
         elif self.shape != other.shape:
             return False
-        elif self.lower_left != other.lower_left:
+        elif np.any(self.lower_left != other.lower_left):
             return False
         else:
             return True
diff --git a/openmc/openmoc_compatible.py b/openmc/openmoc_compatible.py
index 98012fae96..21dc4b6a69 100644
--- a/openmc/openmoc_compatible.py
+++ b/openmc/openmoc_compatible.py
@@ -172,7 +172,9 @@ def get_openmoc_surface(openmc_surface):
         B = openmc_surface.b
         C = openmc_surface.c
         D = openmc_surface.d
-        openmoc_surface = openmoc.Plane(A, B, C, D, surface_id, name)
+
+        # OpenMOC uses the opposite sign on D
+        openmoc_surface = openmoc.Plane(A, B, C, -D, surface_id, name)
 
     elif openmc_surface.type == 'x-plane':
         x0 = openmc_surface.x0
@@ -253,7 +255,9 @@ def get_openmc_surface(openmoc_surface):
         B = openmoc_surface.getB()
         C = openmoc_surface.getC()
         D = openmoc_surface.getD()
-        openmc_surface = openmc.Plane(surface_id, boundary, A, B, C, D, name)
+
+        # OpenMOC uses the opposite sign on D
+        openmc_surface = openmc.Plane(surface_id, boundary, A, B, C, -D, name)
 
     elif openmoc_surface.getSurfaceType() == openmoc.XPLANE:
         openmoc_surface = openmoc.castSurfaceToXPlane(openmoc_surface)
@@ -708,8 +712,7 @@ def get_openmc_lattice(openmoc_lattice):
                 universe_array[x][y][z] = \
                     unique_universes[universe_id]
 
-    universe_array = np.swapaxes(universe_array, 0, 1)
-    universe_array = universe_array[::-1, :, :]
+    universe_array = np.swapaxes(universe_array, 0, 2)
 
     # Convert axially infinite 3D OpenMOC lattice to a 2D OpenMC lattice
     if width[2] == np.finfo(np.float64).max:
diff --git a/openmc/universe.py b/openmc/universe.py
index c955934f2a..d36b167a51 100644
--- a/openmc/universe.py
+++ b/openmc/universe.py
@@ -76,7 +76,7 @@ class Universe(object):
             return False
         elif self.name != other.name:
             return False
-        elif self.cells != other.cells:
+        elif dict.__ne__(self.cells, other.cells):
             return False
         else:
             return True