diff --git a/src/t8_schemes/t8_default/t8_default_pyramid/t8_dpyramid_bits.c b/src/t8_schemes/t8_default/t8_default_pyramid/t8_dpyramid_bits.c
index 3507879f6b..27eca19147 100644
--- a/src/t8_schemes/t8_default/t8_default_pyramid/t8_dpyramid_bits.c
+++ b/src/t8_schemes/t8_default/t8_default_pyramid/t8_dpyramid_bits.c
@@ -27,6 +27,7 @@
 #include <t8_schemes/t8_default/t8_default_tet/t8_dtet_bits.h>
 #include <t8_schemes/t8_default/t8_default_tet/t8_dtet_connectivity.h>
 #include <t8_schemes/t8_default/t8_default_tri/t8_dtri_bits.h>
+#include <t8_eclass.h>
 
 typedef int8_t t8_dpyramid_cube_id_t;
 
@@ -973,7 +974,7 @@ t8_dpyramid_first_descendant_face (const t8_dpyramid_t *p, const int face, t8_dp
   T8_ASSERT (0 <= level && level <= T8_DPYRAMID_MAXLEVEL);
   T8_ASSERT (p->pyramid.level <= level);
   if (t8_dpyramid_shape (p) == T8_ECLASS_TET) {
-    const int corner = t8_dtet_face_corner[face][0];
+    const int corner = t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][0];
     t8_dpyramid_corner_descendant (p, first_desc, corner, level);
   }
   else if (p->pyramid.level == T8_DPYRAMID_MAXLEVEL) {
@@ -1040,7 +1041,8 @@ t8_dpyramid_last_descendant_face (const t8_dpyramid_t *p, const int face, t8_dpy
 
   if (t8_dpyramid_shape (p) == T8_ECLASS_TET) {
     T8_ASSERT (0 <= face && face < T8_DTET_FACES);
-    const int corner = SC_MAX (t8_dtet_face_corner[face][1], t8_dtet_face_corner[face][2]);
+    const int corner = SC_MAX (t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][1],
+                               t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][2]);
     t8_dpyramid_corner_descendant (p, last_desc, corner, level);
   }
   else {
@@ -1395,7 +1397,7 @@ t8_dpyramid_get_face_corner (const t8_dpyramid_t *pyra, int face, int corner)
 {
   T8_ASSERT (0 <= face && face <= T8_DPYRAMID_FACES);
   if (t8_dpyramid_shape (pyra) == T8_ECLASS_TET) {
-    return t8_dtet_face_corner[face][corner];
+    return t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][corner];
   }
   else {
     const int corner_number = t8_dpyramid_face_corner[pyra->pyramid.type - T8_DPYRAMID_FIRST_TYPE][face][corner];
diff --git a/src/t8_schemes/t8_default/t8_default_tet/t8_default_tet.cxx b/src/t8_schemes/t8_default/t8_default_tet/t8_default_tet.cxx
index bc571d361a..3e66122ed0 100644
--- a/src/t8_schemes/t8_default/t8_default_tet/t8_default_tet.cxx
+++ b/src/t8_schemes/t8_default/t8_default_tet/t8_default_tet.cxx
@@ -25,6 +25,7 @@
 #include <t8_schemes/t8_default/t8_default_tet/t8_dtet_bits.h>
 #include <t8_schemes/t8_default/t8_default_tri/t8_dtri_bits.h>
 #include <t8_schemes/t8_default/t8_default_tet/t8_dtet_connectivity.h>
+#include <t8_eclass.h>
 
 /* We want to export the whole implementation to be callable from "C" */
 T8_EXTERN_C_BEGIN ();
@@ -118,7 +119,7 @@ t8_default_scheme_tet_c::t8_element_get_face_corner (const t8_element_t *element
 {
   T8_ASSERT (0 <= face && face < T8_DTET_FACES);
   T8_ASSERT (0 <= corner && corner < 3);
-  return t8_dtet_face_corner[face][corner];
+  return t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][corner];
 }
 
 void
@@ -297,7 +298,7 @@ t8_default_scheme_tet_c::t8_element_first_descendant_face (const t8_element_t *e
   T8_ASSERT (0 <= level && level <= T8_DTET_MAXLEVEL);
 
   /* Compute the first corner of this face */
-  corner = t8_dtet_face_corner[face][0];
+  corner = t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][0];
   /* Compute the descendant in this corner */
   t8_dtet_corner_descendant ((const t8_dtet_t *) elem, (t8_dtet_t *) first_desc, corner, level);
 }
@@ -311,7 +312,8 @@ t8_default_scheme_tet_c::t8_element_last_descendant_face (const t8_element_t *el
   T8_ASSERT (0 <= level && level <= T8_DTET_MAXLEVEL);
 
   /* Compute the last corner of this face */
-  corner = SC_MAX (t8_dtet_face_corner[face][1], t8_dtet_face_corner[face][2]);
+  corner = SC_MAX (t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][1],
+                   t8_face_vertex_to_tree_vertex[T8_ECLASS_TET][face][2]);
   /* Compute the descendant in this corner */
   t8_dtet_corner_descendant ((const t8_dtet_t *) elem, (t8_dtet_t *) last_desc, corner, level);
 }
diff --git a/src/t8_schemes/t8_default/t8_default_tet/t8_dtri_to_dtet.h b/src/t8_schemes/t8_default/t8_default_tet/t8_dtri_to_dtet.h
index 28009478f5..1de3e96545 100644
--- a/src/t8_schemes/t8_default/t8_default_tet/t8_dtri_to_dtet.h
+++ b/src/t8_schemes/t8_default/t8_default_tet/t8_dtri_to_dtet.h
@@ -62,7 +62,6 @@ T8_EXTERN_C_BEGIN ();
 #define t8_dtri_parenttype_Iloc_to_type t8_dtet_parenttype_Iloc_to_type
 #define t8_dtri_parenttype_Iloc_to_cid t8_dtet_parenttype_Iloc_to_cid
 #define t8_dtri_type_cid_to_Iloc t8_dtet_type_cid_to_Iloc
-#define t8_dtri_face_corner t8_dtet_face_corner
 
 /* functions in d8_dtri_bits.h */
 #define t8_dtri_is_equal t8_dtet_is_equal