diff --git a/FIAT/crouzeix_raviart.py b/FIAT/crouzeix_raviart.py
index 0979c9d4..8447a126 100644
--- a/FIAT/crouzeix_raviart.py
+++ b/FIAT/crouzeix_raviart.py
@@ -14,7 +14,6 @@
 from FIAT.check_format_variant import check_format_variant
 from FIAT.quadrature_schemes import create_quadrature
 from FIAT.quadrature import FacetQuadratureRule
-from FIAT.reference_element import make_lattice
 
 
 class CrouzeixRaviartDualSet(dual_set.DualSet):
@@ -24,6 +23,9 @@ def __init__(self, ref_el, degree, variant, interpolant_deg):
         sd = ref_el.get_spatial_dimension()
         top = ref_el.get_topology()
 
+        if degree > 1 and sd != 2:
+            raise NotImplementedError("High-order Crouzeix-Raviart is only implemented on triangles.")
+
         # Initialize empty nodes and entity_ids
         entity_ids = {dim: {entity: [] for entity in top[dim]} for dim in top}
         nodes = []
@@ -61,11 +63,9 @@ def __init__(self, ref_el, degree, variant, interpolant_deg):
                 for i in sorted(top[dim]):
                     cur = len(nodes)
                     if dim == sd-1 and dim != 0:
-                        verts = ref_el.get_vertices_of_subcomplex(top[dim][i])
-                        pts = make_lattice(verts, degree-1, variant="gl")
+                        pts = ref_el.make_points(dim, i, degree-1, variant="gl", interior=0)
                     else:
                         pts = ref_el.make_points(dim, i, degree, variant="gll")
-
                     nodes.extend(functional.PointEvaluation(ref_el, x) for x in pts)
                     entity_ids[dim][i].extend(range(cur, len(nodes)))
 
diff --git a/FIAT/reference_element.py b/FIAT/reference_element.py
index 7d9ff296..b4cd2c63 100644
--- a/FIAT/reference_element.py
+++ b/FIAT/reference_element.py
@@ -510,7 +510,7 @@ def compute_face_edge_tangents(self, dim, entity_id):
                 v1.append(dest)
         return vert_coords[v1] - vert_coords[v0]
 
-    def make_points(self, dim, entity_id, order, variant=None):
+    def make_points(self, dim, entity_id, order, variant=None, interior=1):
         """Constructs a lattice of points on the entity_id:th
         facet of dimension dim.  Order indicates how many points to
         include in each direction."""
@@ -520,7 +520,7 @@ def make_points(self, dim, entity_id, order, variant=None):
             entity_verts = \
                 self.get_vertices_of_subcomplex(
                     self.get_topology()[dim][entity_id])
-            return make_lattice(entity_verts, order, 1, variant=variant)
+            return make_lattice(entity_verts, order, interior=interior, variant=variant)
         else:
             raise ValueError("illegal dimension")