diff --git a/.github/workflows/run-tests.yml b/.github/workflows/run-tests.yml
index 7b49525..ab7ad58 100644
--- a/.github/workflows/run-tests.yml
+++ b/.github/workflows/run-tests.yml
@@ -49,6 +49,11 @@ jobs:
           chmod +x examples.sh
           ./examples.sh
 
+  run-tests-python:
+    name: Run Python tests
+    runs-on: ubuntu-latest
+    strategy:
+
   check-dependencies:
     name: Check dependencies
     runs-on: ubuntu-latest
diff --git a/python/ndelement/reference_cell.py b/python/ndelement/reference_cell.py
index 7514db4..576e7bf 100644
--- a/python/ndelement/reference_cell.py
+++ b/python/ndelement/reference_cell.py
@@ -1,5 +1,9 @@
-"""Types."""
-from ._ndelementrs import lib as _lib
+"""Reference cell information."""
+import typing
+import ctypes
+import numpy as np
+import numpy.typing as npt
+from ._ndelementrs import lib as _lib, ffi as _ffi
 from enum import Enum
 
 
@@ -16,6 +20,99 @@ class ReferenceCellType(Enum):
 
 
 def dim(cell: ReferenceCellType) -> int:
-    """The topological dimension of a reference cell."""
+    """Get the topological dimension of a reference cell."""
     return _lib.dim(cell.value)
 
+
+def is_simplex(cell: ReferenceCellType) -> bool:
+    """Check if a reference cell is a simplex."""
+    return _lib.is_simplex(cell.value)
+
+
+def vertices(cell: ReferenceCellType, dtype: str = np.float64) -> npt.NDArray:
+    """Get the vertices of a reference cell."""
+    vertices = np.empty((entity_counts(cell)[0], dim(cell)), dtype=dtype)
+    if dtype == np.float64:
+        _lib.vertices_f64(cell.value, _ffi.cast("double*", vertices.ctypes.data))
+    elif dtype == np.float32:
+        _lib.vertices_f32(cell.value, _ffi.cast("float*", vertices.ctypes.data))
+    else:
+        raise TypeError(f"Unsupported dtype: {dtype}")
+    return vertices
+
+
+def midpoint(cell: ReferenceCellType, dtype: str = np.float64) -> npt.NDArray:
+    """Get the midpoint of a reference cell."""
+    point = np.empty(dim(cell), dtype=dtype)
+    if dtype == np.float64:
+        _lib.midpoint_f64(cell.value, _ffi.cast("double*", point.ctypes.data))
+    elif dtype == np.float32:
+        _lib.midpoint_f32(cell.value, _ffi.cast("float*", point.ctypes.data))
+    else:
+        raise TypeError(f"Unsupported dtype: {dtype}")
+    return point
+
+
+def edges(cell: ReferenceCellType) -> typing.List[npt.NDArray[int]]:
+    """Get the edges of a reference cell."""
+    edges = []
+    e = np.empty(2 * entity_counts(cell)[1], dtype=int)
+    _lib.faces(cell.value, _ffi.cast("uintptr_t* ", e.ctypes.data))
+    for i in range(entity_counts(cell)[1]):
+        edges.append(e[2*i:2*i+2])
+    return edges
+
+
+def faces(cell: ReferenceCellType) -> typing.List[npt.NDArray[int]]:
+    """Get the faces of a reference cell."""
+    faces = []
+    flen = 0
+    for t in entity_types(cell)[2]:
+        flen += entity_counts(t)[0]
+    f = np.empty(flen, dtype=int)
+    _lib.faces(cell.value, _ffi.cast("uintptr_t* ", f.ctypes.data))
+    start = 0
+    for t in entity_types(cell)[2]:
+        n = entity_counts(t)[0]
+        faces.append(f[start:start+n])
+        start += n
+    return faces
+
+
+def volumes(cell: ReferenceCellType) -> typing.List[npt.NDArray[int]]:
+    """Get the volumes of a reference cell."""
+    volumes = []
+    vlen = 0
+    for t in entity_types(cell)[3]:
+        vlen += entity_counts(t)[0]
+    v = np.empty(vlen, dtype=int)
+    _lib.volumes(cell.value, _ffi.cast("uintptr_t* ", v.ctypes.data))
+    start = 0
+    for t in entity_types(cell)[3]:
+        n = entity_counts(t)[0]
+        volumes.append(v[start:start+n])
+        start += n
+    return volumes
+
+
+def entity_types(cell: ReferenceCellType) -> typing.List[typing.List[ReferenceCellType]]:
+    """Get the types of the sub-entities of a reference cell."""
+    # TODO: should int be uintptr_t?
+    t = np.empty(sum(entity_counts(cell)), dtype=int)
+    _lib.entity_types(cell.value, _ffi.cast("uintptr_t* ", t.ctypes.data))
+    types = []
+    start = 0
+    for n in entity_counts(cell):
+        types.append([ReferenceCellType(i) for i in t[start:start+n]])
+        start += n
+    return types
+
+
+def entity_counts(cell: ReferenceCellType) -> npt.NDArray[int]:
+    """Get the number of the sub-entities of each dimension for a reference cell."""
+    counts = np.empty(4, dtype=int)
+    _lib.entity_counts(cell.value, _ffi.cast("uintptr_t* ", counts.ctypes.data))
+    return counts
+
+
+# TODO: connectivity
diff --git a/python/test/test_reference_cell.py b/python/test/test_reference_cell.py
index a90e83e..66bc03d 100644
--- a/python/test/test_reference_cell.py
+++ b/python/test/test_reference_cell.py
@@ -1,4 +1,6 @@
-from ndelement.reference_cell import dim, ReferenceCellType
+import pytest
+import numpy as np
+from ndelement.reference_cell import dim, ReferenceCellType, midpoint, vertices
 
 
 def test_dim():
@@ -8,3 +10,25 @@ def test_dim():
     assert dim(ReferenceCellType.Quadrilateral) == 2
     assert dim(ReferenceCellType.Tetrahedron) == 3
     assert dim(ReferenceCellType.Hexahedron) == 3
+
+
+def test_midpoint():
+    assert np.allclose(midpoint(ReferenceCellType.Interval), [0.5])
+    assert np.allclose(midpoint(ReferenceCellType.Triangle), [1 / 3, 1 / 3])
+    assert np.allclose(midpoint(ReferenceCellType.Quadrilateral), [1 / 2, 1 / 2])
+    assert np.allclose(midpoint(ReferenceCellType.Tetrahedron), [1 / 4, 1 / 4, 1 / 4])
+    assert np.allclose(midpoint(ReferenceCellType.Hexahedron), [1 / 2, 1 / 2, 1 / 2])
+
+
+@pytest.mark.parametrize("cell", [
+    ReferenceCellType.Interval,
+    ReferenceCellType.Triangle,
+    ReferenceCellType.Quadrilateral,
+    ReferenceCellType.Tetrahedron,
+    ReferenceCellType.Hexahedron,
+])
+def test_vertices_and_midpoint(cell):
+    v = vertices(cell)
+    m = midpoint(cell)
+
+    assert np.allclose(sum(i for i in v) / v.shape[0], m)
diff --git a/src/bindings.rs b/src/bindings.rs
index 9ca9db8..2805221 100644
--- a/src/bindings.rs
+++ b/src/bindings.rs
@@ -3,13 +3,101 @@
 
 pub mod reference_cell {
     use crate::types::ReferenceCellType;
+    use crate::reference_cell;
+    use rlst::RlstScalar;
 
     #[no_mangle]
     pub unsafe extern "C" fn dim(cell: u8) -> usize {
-        crate::reference_cell::dim(ReferenceCellType::from(cell).expect("Invalid cell type"))
+        reference_cell::dim(ReferenceCellType::from(cell).expect("Invalid cell type"))
     }
     #[no_mangle]
     pub unsafe extern "C" fn is_simplex(cell: u8) -> bool {
-        crate::reference_cell::is_simplex(ReferenceCellType::from(cell).expect("Invalid cell type"))
+        reference_cell::is_simplex(ReferenceCellType::from(cell).expect("Invalid cell type"))
+    }
+    unsafe fn vertices<T: RlstScalar<Real=T>>(cell: u8, vs: *mut T) {
+        let mut i = 0;
+        for v in reference_cell::vertices::<T>(ReferenceCellType::from(cell).expect("Invalid cell type")) {
+            for c in v {
+                *vs.add(i) = c;
+                i += 1;
+            }
+        }
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn vertices_f32(cell: u8, vs: *mut f32) {
+        vertices(cell, vs);
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn vertices_f64(cell: u8, vs: *mut f64) {
+        vertices(cell, vs);
+    }
+    unsafe fn midpoint<T: RlstScalar<Real=T>>(cell: u8, pt: *mut T) {
+        let pt = pt as *mut T;
+        for (i, c) in reference_cell::midpoint(ReferenceCellType::from(cell).expect("Invalid cell type")).iter().enumerate() {
+            *pt.add(i) = *c;
+        }
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn midpoint_f32(cell: u8, pt: *mut f32) {
+        midpoint(cell, pt);
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn midpoint_f64(cell: u8, pt: *mut f64) {
+        midpoint(cell, pt);
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn edges(cell: u8, es: *mut usize) {
+        let mut i = 0;
+        for e in reference_cell::edges(ReferenceCellType::from(cell).expect("Invalid cell type")) {
+            for v in e {
+                *es.add(i) = v;
+                i += 1
+            }
+        }
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn faces(cell: u8, es: *mut usize) {
+        let mut i = 0;
+        for e in reference_cell::faces(ReferenceCellType::from(cell).expect("Invalid cell type")) {
+            for v in e {
+                *es.add(i) = v;
+                i += 1
+            }
+        }
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn volumes(cell: u8, es: *mut usize) {
+        let mut i = 0;
+        for e in reference_cell::volumes(ReferenceCellType::from(cell).expect("Invalid cell type")) {
+            for v in e {
+                *es.add(i) = v;
+                i += 1
+            }
+        }
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn entity_types(cell: u8, et: *mut u8) {
+        let mut i = 0;
+        for es in reference_cell::entity_types(ReferenceCellType::from(cell).expect("Invalid cell type")) {
+            for e in es {
+                *et.add(i) = e as u8;
+                i += 1
+            }
+        }
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn entity_counts(cell: u8, ec: *mut usize) {
+        for (i, e) in reference_cell::entity_counts(ReferenceCellType::from(cell).expect("Invalid cell type")).iter().enumerate() {
+            *ec.add(i) = *e;
+        }
+    }
+    pub unsafe extern "C" fn connetivity_size(cell: u8, dim0: usize, index0: usize, dim1: usize) -> usize {
+        reference_cell::connectivity(ReferenceCellType::from(cell).expect("Invalid cell type"))[dim0][index0][dim1].len()
+    }
+    #[no_mangle]
+    pub unsafe extern "C" fn connetivity(cell: u8, dim0: usize, index0: usize, dim1: usize, c: *mut usize) {
+        for (i, j) in reference_cell::connectivity(ReferenceCellType::from(cell).expect("Invalid cell type"))[dim0][index0][dim1].iter().enumerate() {
+            *c.add(i) = *j;
+        }
     }
 }
diff --git a/src/reference_cell.rs b/src/reference_cell.rs
index 9e15d2a..5884ece 100644
--- a/src/reference_cell.rs
+++ b/src/reference_cell.rs
@@ -87,7 +87,7 @@ pub fn midpoint<T: RlstScalar<Real = T>>(cell: ReferenceCellType) -> Vec<T> {
         ReferenceCellType::Interval => vec![half],
         ReferenceCellType::Triangle => vec![third; 2],
         ReferenceCellType::Quadrilateral => vec![half; 2],
-        ReferenceCellType::Tetrahedron => vec![T::from(1.0).unwrap() / T::from(6.0).unwrap(); 3],
+        ReferenceCellType::Tetrahedron => vec![T::from(1.0).unwrap() / T::from(4.0).unwrap(); 3],
         ReferenceCellType::Hexahedron => vec![half; 3],
         ReferenceCellType::Prism => vec![third, third, half],
         ReferenceCellType::Pyramid => vec![