diff --git a/src/darsia/utils/grid.py b/src/darsia/utils/grid.py
index 00b6f696..6ba078da 100644
--- a/src/darsia/utils/grid.py
+++ b/src/darsia/utils/grid.py
@@ -244,40 +244,40 @@ def _setup(self) -> None:
             self.cell_corner_indices[self.faces[0], 1, 0] = 0
 
         elif self.dim == 2:
-            self.cell_corner_indices[self.faces[0], 0, 0] = 3
+            self.cell_corner_indices[self.faces[0], 0, 0] = 1
             self.cell_corner_indices[self.faces[0], 0, 1] = 2
             self.cell_corner_indices[self.faces[0], 1, 0] = 0
-            self.cell_corner_indices[self.faces[0], 1, 1] = 1
-            self.cell_corner_indices[self.faces[1], 0, 0] = 1
+            self.cell_corner_indices[self.faces[0], 1, 1] = 3
+            self.cell_corner_indices[self.faces[1], 0, 0] = 3
             self.cell_corner_indices[self.faces[1], 0, 1] = 2
             self.cell_corner_indices[self.faces[1], 1, 0] = 0
-            self.cell_corner_indices[self.faces[1], 1, 1] = 3
+            self.cell_corner_indices[self.faces[1], 1, 1] = 1
 
         elif self.dim == 3:
-            self.cell_corner_indices[self.faces[0], 0, 0] = 3
+            self.cell_corner_indices[self.faces[0], 0, 0] = 1
             self.cell_corner_indices[self.faces[0], 0, 1] = 2
-            self.cell_corner_indices[self.faces[0], 0, 2] = 7
+            self.cell_corner_indices[self.faces[0], 0, 2] = 5
             self.cell_corner_indices[self.faces[0], 0, 3] = 6
             self.cell_corner_indices[self.faces[0], 1, 0] = 0
-            self.cell_corner_indices[self.faces[0], 1, 1] = 1
+            self.cell_corner_indices[self.faces[0], 1, 1] = 3
             self.cell_corner_indices[self.faces[0], 1, 2] = 4
-            self.cell_corner_indices[self.faces[0], 1, 3] = 5
-            self.cell_corner_indices[self.faces[1], 0, 0] = 1
+            self.cell_corner_indices[self.faces[0], 1, 3] = 7
+            self.cell_corner_indices[self.faces[1], 0, 0] = 3
             self.cell_corner_indices[self.faces[1], 0, 1] = 2
-            self.cell_corner_indices[self.faces[1], 0, 2] = 5
+            self.cell_corner_indices[self.faces[1], 0, 2] = 7
             self.cell_corner_indices[self.faces[1], 0, 3] = 6
             self.cell_corner_indices[self.faces[1], 1, 0] = 0
-            self.cell_corner_indices[self.faces[1], 1, 1] = 3
+            self.cell_corner_indices[self.faces[1], 1, 1] = 1
             self.cell_corner_indices[self.faces[1], 1, 2] = 4
-            self.cell_corner_indices[self.faces[1], 1, 3] = 7
+            self.cell_corner_indices[self.faces[1], 1, 3] = 5
             self.cell_corner_indices[self.faces[2], 0, 0] = 4
-            self.cell_corner_indices[self.faces[2], 0, 1] = 7
+            self.cell_corner_indices[self.faces[2], 0, 1] = 5
             self.cell_corner_indices[self.faces[2], 0, 2] = 6
-            self.cell_corner_indices[self.faces[2], 0, 3] = 5
+            self.cell_corner_indices[self.faces[2], 0, 3] = 7
             self.cell_corner_indices[self.faces[2], 1, 0] = 0
-            self.cell_corner_indices[self.faces[2], 1, 1] = 3
+            self.cell_corner_indices[self.faces[2], 1, 1] = 1
             self.cell_corner_indices[self.faces[2], 1, 2] = 2
-            self.cell_corner_indices[self.faces[2], 1, 3] = 1
+            self.cell_corner_indices[self.faces[2], 1, 3] = 3
 
 
 def generate_grid(image: darsia.Image) -> Grid: