diff --git a/src/io4dolfinx/backends/pyvista/backend.py b/src/io4dolfinx/backends/pyvista/backend.py
index 261c47a..77372b6 100644
--- a/src/io4dolfinx/backends/pyvista/backend.py
+++ b/src/io4dolfinx/backends/pyvista/backend.py
@@ -22,28 +22,10 @@
 from io4dolfinx.utils import check_file_exists
 
 from .. import FileMode, ReadMode
+from ..vtk_cell_types import _arbitrary_lagrange_vtk, _cell_degree, _first_order_vtk
 
 # Cell types can be found at
 # https://vtk.org/doc/nightly/html/vtkCellType_8h_source.html
-_first_order_vtk = {
-    1: "point",
-    3: "interval",
-    5: "triangle",
-    9: "quadrilateral",
-    10: "tetrahedron",
-    12: "hexahedron",
-}
-
-_arbitrary_lagrange_vtk = {
-    68: "interval",
-    69: "triangle",
-    70: "quadrilateral",
-    71: "tetrahedron",
-    72: "hexahedron",
-    73: "prism",
-    74: "pyramid",
-}
-
 _quadratric_vtk = {
     21: "interval",
     22: "triangle",
@@ -56,52 +38,6 @@
 read_mode = ReadMode.serial
 
 
-def _cell_degree(ct: str, num_nodes: int) -> int:
-    if ct == "point":
-        return 1
-    elif ct == "interval":
-        return int(num_nodes - 1)
-    elif ct == "triangle":
-        n = (np.sqrt(1 + 8 * num_nodes) - 1) / 2
-        if 2 * num_nodes != n * (n + 1):
-            raise ValueError(f"Unknown triangle layout. Number of nodes: {num_nodes}")
-        return int(n - 1)
-    elif ct == "tetrahedron":
-        n = 0
-        while n * (n + 1) * (n + 2) < 6 * num_nodes:
-            n += 1
-        if n * (n + 1) * (n + 2) != 6 * num_nodes:
-            raise ValueError(f"Unknown tetrahedron layout. Number of nodes: {num_nodes}")
-        return int(n - 1)
-
-    elif ct == "quadrilateral":
-        n = np.sqrt(num_nodes)
-        if num_nodes != n * n:
-            raise ValueError(f"Unknown quadrilateral layout. Number of nodes: {num_nodes}")
-        return int(n - 1)
-    elif ct == "hexahedron":
-        n = np.cbrt(num_nodes)
-        if num_nodes != n * n * n:
-            raise ValueError(f"Unknown hexahedron layout. Number of nodes: {num_nodes}")
-        return int(n - 1)
-    elif ct == "prism":
-        if num_nodes == 6:
-            return 1
-        elif num_nodes == 15:
-            return 2
-        else:
-            raise ValueError(f"Unknown prism layout. Number of nodes: {num_nodes}")
-    elif ct == "pyramid":
-        if num_nodes == 5:
-            return 1
-        elif num_nodes == 13:
-            return 2
-        else:
-            raise ValueError(f"Unknown pyramid layout. Number of nodes: {num_nodes}")
-    else:
-        raise ValueError(f"Unknown cell type {ct} with {num_nodes=}.")
-
-
 def get_default_backend_args(arguments: dict[str, Any] | None) -> dict[str, Any]:
     """Get default backend arguments given a set of input arguments.
 
diff --git a/src/io4dolfinx/backends/vtk_cell_types.py b/src/io4dolfinx/backends/vtk_cell_types.py
new file mode 100644
index 0000000..aa0bf45
--- /dev/null
+++ b/src/io4dolfinx/backends/vtk_cell_types.py
@@ -0,0 +1,65 @@
+import numpy as np
+
+# Cell types can be found at
+# https://vtk.org/doc/nightly/html/vtkCellType_8h_source.html
+
+_first_order_vtk = {
+    1: "point",
+    3: "interval",
+    5: "triangle",
+    9: "quadrilateral",
+    10: "tetrahedron",
+    12: "hexahedron",
+}
+
+_arbitrary_lagrange_vtk = {
+    68: "interval",
+    69: "triangle",
+    70: "quadrilateral",
+    71: "tetrahedron",
+    72: "hexahedron",
+    73: "prism",
+    74: "pyramid",
+}
+
+
+def _cell_degree(cell_type: str, num_nodes: int) -> int:
+    if cell_type == "point":
+        return 1
+    elif cell_type == "interval":
+        return int(num_nodes - 1)
+    elif cell_type == "triangle":
+        degree = (np.sqrt(1 + 8 * num_nodes) - 1) / 2
+        if 2 * num_nodes != degree * (degree + 1):
+            raise ValueError(f"Unknown triangle layout. Number of nodes: {num_nodes}")
+        return int(degree - 1)
+    elif cell_type == "tetrahedron":
+        degree = 0
+        while degree * (degree + 1) * (degree + 2) < 6 * num_nodes:
+            degree += 1
+        if degree * (degree + 1) * (degree + 2) != 6 * num_nodes:
+            raise ValueError(f"Unknown tetrahedron layout. Number of nodes: {num_nodes}")
+        return int(degree - 1)
+    elif cell_type == "quadrilateral":
+        degree = np.sqrt(num_nodes)
+        if num_nodes != degree * degree:
+            raise ValueError(f"Unknown quadrilateral layout. Number of nodes: {num_nodes}")
+        return int(degree - 1)
+    elif cell_type == "hexahedron":
+        degree = np.cbrt(num_nodes)
+        if num_nodes != degree * degree * degree:
+            raise ValueError(f"Unknown hexahedron layout. Number of nodes: {num_nodes}")
+        return int(degree - 1)
+    elif cell_type == "prism":
+        if num_nodes == 6:
+            return 1
+        elif num_nodes == 15:
+            return 2
+        raise ValueError(f"Unknown prism layout. Number of nodes: {num_nodes}")
+    elif cell_type == "pyramid":
+        if num_nodes == 5:
+            return 1
+        elif num_nodes == 13:
+            return 2
+        raise ValueError(f"Unknown pyramid layout. Number of nodes: {num_nodes}")
+    raise ValueError(f"Unknown cell type {cell_type} with {num_nodes=}.")
diff --git a/src/io4dolfinx/backends/vtkhdf/backend.py b/src/io4dolfinx/backends/vtkhdf/backend.py
index e4f1737..f3297d8 100644
--- a/src/io4dolfinx/backends/vtkhdf/backend.py
+++ b/src/io4dolfinx/backends/vtkhdf/backend.py
@@ -18,7 +18,7 @@
 
 from .. import FileMode, ReadMode
 from ..h5py.backend import convert_file_mode, h5pyfile
-from ..pyvista.backend import _arbitrary_lagrange_vtk, _cell_degree, _first_order_vtk
+from ..vtk_cell_types import _arbitrary_lagrange_vtk, _cell_degree, _first_order_vtk
 
 read_mode = ReadMode.parallel
 
@@ -349,7 +349,7 @@ def write_attributes(
         attributes: Dictionary of attributes to write
         backend_args: Arguments to backend
     """
-    raise NotImplementedError("The Pyvista backend cannot write attributes.")
+    raise NotImplementedError("The VTKHDF backend cannot write attributes.")
 
 
 def read_attributes(
@@ -369,7 +369,7 @@ def read_attributes(
     Returns:
         Dictionary of attributes read from file
     """
-    raise NotImplementedError("The Pyvista backend cannot read attributes.")
+    raise NotImplementedError("The VTKHDF backend cannot read attributes.")
 
 
 def read_timestamps(
@@ -1000,7 +1000,7 @@ def read_dofmap(
     Returns:
         Dofmap as an AdjacencyList
     """
-    raise NotImplementedError("The Pyvista backend cannot make checkpoints.")
+    raise NotImplementedError("The VTKHDF backend cannot make checkpoints.")
 
 
 def read_dofs(
@@ -1024,7 +1024,7 @@ def read_dofs(
         and the global starting point on the process.
         Process 0 has [0, M), process 1 [M, N), process 2 [N, O) etc.
     """
-    raise NotImplementedError("The Pyvista backend cannot make checkpoints.")
+    raise NotImplementedError("The VTKHDF backend cannot make checkpoints.")
 
 
 def read_cell_perms(