diff --git a/opensm/opensm/osm_torus.c b/opensm/opensm/osm_torus.c
index 8aa0c18..3257ec4 100644
--- a/opensm/opensm/osm_torus.c
+++ b/opensm/opensm/osm_torus.c
@@ -4503,3 +4503,2427 @@ bool handle_case_0x7f0(struct torus *t, int i, int j, int k)
 
 	return handle_case_0x7f8(t, i, j, k);
 }
+
+/*
+ * Handle the cases where three corners on a single face are missing.
+ */
+
+
+/*
+ * 3D case 0x707:                           O
+ *                                        . . .
+ *  b0:                                 .   .   .
+ *  b1:                               .     .     .
+ *  b2:                             .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]          .           .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .
+ *  b7: t->sw[i+1][j+1][k+1]              .   .
+ *                                          O
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x707(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x707, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x707, i, j, k, i, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x70b:                           O
+ *                                        .   .
+ *  b0:                                 .       .
+ *  b1:                               .           .
+ *  b2: t->sw[i  ][j+1][k  ]        .               .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .           .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .       .   .
+ *                                .         O
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x70b(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70b, i, j, k, i, j, k);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70b, i, j, k, ip1, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x70d:                           O
+ *                                        .   .
+ *  b0:                                 .       .
+ *  b1: t->sw[i+1][j  ][k  ]          .           .
+ *  b2:                             .               .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]          .           .   .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]              .   .       .
+ *                                          O         .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x70d(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70d, i, j, k, i, j, k);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70d, i, j, k, ip1, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x70e:                           O
+ *                                        .   .
+ *  b0: t->sw[i  ][j  ][k  ]            .       .
+ *  b1:                               .           .
+ *  b2:                             .               .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]          .           .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .
+ *  b7: t->sw[i+1][j+1][k+1]              .   .
+ *                                          O
+ *                                O         .         O
+ *                                          .
+ *                                          .
+ *                                          .
+ *                                          .
+ *                                          @
+ */
+static
+bool handle_case_0x70e(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70e, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70e, i, j, k, i, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x713:                           O
+ *                                        . . .
+ *  b0:                                 .   .   .
+ *  b1:                               .     .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                           .         O
+ *  b5: t->sw[i+1][j  ][k+1]      .       .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .
+ *                                . .       O
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x713(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x713, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x713, i, j, k, i, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x715:                           O
+ *                                        . . .
+ *  b0:                                 .   .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .     .
+ *  b2:                             .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                                     O         .
+ *  b5: t->sw[i+1][j  ][k+1]                  .       .
+ *  b6: t->sw[i  ][j+1][k+1]                    .     .
+ *  b7: t->sw[i+1][j+1][k+1]                      .   .
+ *                                          O       . .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x715(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x715, i, j, k, i, jp1, k);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x715, i, j, k, i, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x723:                           O
+ *                                        . .
+ *  b0:                                 .   .
+ *  b1:                               .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .   .
+ *                                . .       O
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x723(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x723, i, j, k, i, j, k);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x723, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x72a:                           O
+ *                                        .
+ *  b0: t->sw[i  ][j  ][k  ]            .
+ *  b1:                               .
+ *  b2: t->sw[i  ][j+1][k  ]        .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .       .
+ *                                .         O
+ *                                O         .         O
+ *                                  .       .
+ *                                    .     .
+ *                                      .   .
+ *                                        . .
+ *                                          @
+ */
+static
+bool handle_case_0x72a(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x72a, i, j, k, ip1, jp1, k);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x72a, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x731:                           O
+ *                                        . .
+ *  b0:                                 .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                           .         O
+ *  b5:                           .       .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .           .
+ *                                . .       O       .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x731(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x731, i, j, k, i, j, k);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x731, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x732:                           O
+ *                                        . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .
+ *  b1:                               .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                           .         O
+ *  b5:                           .       .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .
+ *                                . .       O
+ *                                O                   O
+ *                                  .
+ *                                    .
+ *                                      .
+ *                                        .
+ *                                          @
+ */
+static
+bool handle_case_0x732(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x732, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x732, i, j, k, i, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x745:                           O
+ *                                          . .
+ *  b0:                                     .   .
+ *  b1: t->sw[i+1][j  ][k  ]                .     .
+ *  b2:                                     .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]                  .   .   .
+ *  b6:                                         .     .
+ *  b7: t->sw[i+1][j+1][k+1]                  .   .   .
+ *                                          O       . .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x745(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x745, i, j, k, i, j, k);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x745, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x74c:                           O
+ *                                            .
+ *  b0: t->sw[i  ][j  ][k  ]                    .
+ *  b1: t->sw[i+1][j  ][k  ]                      .
+ *  b2:                                             .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]                      .   .
+ *  b6:                                         .     .
+ *  b7: t->sw[i+1][j+1][k+1]                  .       .
+ *                                          O         .
+ *                                O         .         O
+ *                                          .       .
+ *                                          .     .
+ *                                          .   .
+ *                                          . .
+ *                                          @
+ */
+static
+bool handle_case_0x74c(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x74c, i, j, k, ip1, jp1, k);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x74c, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x751:                           O
+ *                                          . .
+ *  b0:                                     .   .
+ *  b1: t->sw[i+1][j  ][k  ]                .     .
+ *  b2: t->sw[i  ][j+1][k  ]                .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                                     O         .
+ *  b5: t->sw[i+1][j  ][k+1]              .   .       .
+ *  b6:                                 .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]          .           .   .
+ *                                  .       O       . .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x751(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x751, i, j, k, i, j, k);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x751, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x754:                           O
+ *                                          . .
+ *  b0: t->sw[i  ][j  ][k  ]                .   .
+ *  b1: t->sw[i+1][j  ][k  ]                .     .
+ *  b2:                                     .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                                     O         .
+ *  b5: t->sw[i+1][j  ][k+1]                  .       .
+ *  b6:                                         .     .
+ *  b7: t->sw[i+1][j+1][k+1]                      .   .
+ *                                          O       . .
+ *                                O                   O
+ *                                                  .
+ *                                                .
+ *                                              .
+ *                                            .
+ *                                          @
+ */
+static
+bool handle_case_0x754(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x754, i, j, k, i, jp1, k);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x754, i, j, k, i, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x770:                           O
+ *                                          .
+ *  b0: t->sw[i  ][j  ][k  ]                .
+ *  b1: t->sw[i+1][j  ][k  ]                .
+ *  b2: t->sw[i  ][j+1][k  ]                .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                                     O
+ *  b5:                                   .   .
+ *  b6:                                 .       .
+ *  b7: t->sw[i+1][j+1][k+1]          .           .
+ *                                  .       O       .
+ *                                O                   O
+ *                                  .               .
+ *                                    .           .
+ *                                      .       .
+ *                                        .   .
+ *                                          @
+ */
+static
+bool handle_case_0x770(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x770, i, j, k, ip1, j, kp1);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x770, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x78a:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1:
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .           .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7:                           .       .   .
+ *                                .         O
+ *                                O         .         O
+ *                                  .       .
+ *                                    .     .
+ *                                      .   .
+ *                                        . .
+ *                                          @
+ */
+static
+bool handle_case_0x78a(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x78a, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x78a, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x78c:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2:
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]          .           .   .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .     .
+ *  b7:                                   .   .       .
+ *                                          O         .
+ *                                O         .         O
+ *                                          .       .
+ *                                          .     .
+ *                                          .   .
+ *                                          . .
+ *                                          @
+ */
+static
+bool handle_case_0x78c(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x78c, i, j, k, i, jp1, k);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x78c, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7a2:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1:
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7:                           .   .   .
+ *                                . .       O
+ *                                O         .         O
+ *                                  .       .
+ *                                    .     .
+ *                                      .   .
+ *                                        . .
+ *                                          @
+ */
+static
+bool handle_case_0x7a2(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7a2, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][kp1],
+					      t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7a2, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7a8:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[ip1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7:                           .       .
+ *                                .         O
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x7a8(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[i][j][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7a8, i, j, k, ip1, jp1, k);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][j][k],
+					      t->sw[ip1][j][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7a8, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7b0:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4:                           .         O
+ *  b5:                           .       .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7:                           .   .           .
+ *                                . .       O       .
+ *                                O                   O
+ *                                  .               .
+ *                                    .           .
+ *                                      .       .
+ *                                        .   .
+ *                                          @
+ */
+static
+bool handle_case_0x7b0(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7b0, i, j, k, i, j, kp1);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][kp1],
+					      t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7b0, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7c4:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2:
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]                  .   .   .
+ *  b6:                                         .     .
+ *  b7:                                       .   .   .
+ *                                          O       . .
+ *                                O         .         O
+ *                                          .       .
+ *                                          .     .
+ *                                          .   .
+ *                                          . .
+ *                                          @
+ */
+static
+bool handle_case_0x7c4(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7c4, i, j, k, i, jp1, k);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7c4, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7c8:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]                      .   .
+ *  b6:                                         .     .
+ *  b7:                                       .       .
+ *                                          O         .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x7c8(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[i][j][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7c8, i, j, k, ip1, jp1, k);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][j][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7c8, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7d0:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4:                                     O         .
+ *  b5: t->sw[i+1][j  ][k+1]              .   .       .
+ *  b6:                                 .       .     .
+ *  b7:                               .           .   .
+ *                                  .       O       . .
+ *                                O                   O
+ *                                  .               .
+ *                                    .           .
+ *                                      .       .
+ *                                        .   .
+ *                                          @
+ */
+static
+bool handle_case_0x7d0(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7d0, i, j, k, i, j, kp1);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7d0, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7e0:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4: t->sw[i  ][j  ][k+1]                O
+ *  b5:                                   .   .
+ *  b6:                                 .       .
+ *  b7:                               .           .
+ *                                  .       O       .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x7e0(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][j][k],
+					      t->sw[ip1][j][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7e0, i, j, k, ip1, j, kp1);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][j][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7e0, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * Handle the cases where two corners on a single edge are missing.
+ */
+
+/*
+ * 3D case 0x703:                           O
+ *                                        . . .
+ *  b0:                                 .   .   .
+ *  b1:                               .     .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .   .       .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .   .   .
+ *                                . .       O
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x703(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x703, i, j, k, i, j, k);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x703, i, j, k, ip1, j, k);
+	return false;
+}
+
+/*
+ * 3D case 0x705:                           O
+ *                                        . . .
+ *  b0:                                 .   .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .     .
+ *  b2:                             .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]          .       .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]              .   .   .   .
+ *                                          O       . .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x705(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x705, i, j, k, i, j, k);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x705, i, j, k, i, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x70a:                           O
+ *                                        . . .
+ *  b0: t->sw[i  ][j  ][k  ]            .       .
+ *  b1:                               .           .
+ *  b2: t->sw[i  ][j+1][k  ]        .               .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .           .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .       .   .
+ *                                .         O
+ *                                O         .         O
+ *                                  .       .
+ *                                    .     .
+ *                                      .   .
+ *                                        . .
+ *                                          @
+ */
+static
+bool handle_case_0x70a(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70a, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70a, i, j, k, ip1, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x70c:                           O
+ *                                        .   .
+ *  b0: t->sw[i  ][j  ][k  ]            .       .
+ *  b1: t->sw[i+1][j  ][k  ]          .           .
+ *  b2:                             .               .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]          .           .   .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]              .   .       .
+ *                                          O         .
+ *                                O         .         O
+ *                                          .       .
+ *                                          .     .
+ *                                          .   .
+ *                                          . .
+ *                                          @
+ */
+static
+bool handle_case_0x70c(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70c, i, j, k, i, jp1, k);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x70c, i, j, k, ip1, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x711:                           O
+ *                                        . . .
+ *  b0:                                 .   .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                           .         O         .
+ *  b5: t->sw[i+1][j  ][k+1]      .       .   .       .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .           .   .
+ *                                . .       O       . .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x711(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x711, i, j, k, i, j, k);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x711, i, j, k, i, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x722:                           O
+ *                                        . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .
+ *  b1:                               .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .   .
+ *                                . .       O
+ *                                O         .         O
+ *                                  .       .
+ *                                    .     .
+ *                                      .   .
+ *                                        . .
+ *                                          @
+ */
+static
+bool handle_case_0x722(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x722, i, j, k, ip1, j, k);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x722, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x730:                           O
+ *                                        . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                           .         O
+ *  b5:                           .       .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .           .
+ *                                . .       O       .
+ *                                O                   O
+ *                                  .               .
+ *                                    .           .
+ *                                      .       .
+ *                                        .   .
+ *                                          @
+ */
+static
+bool handle_case_0x730(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][jp1][k],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x730, i, j, k, i, j, kp1);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x730, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x744:                           O
+ *                                          . .
+ *  b0: t->sw[i  ][j  ][k  ]                .   .
+ *  b1: t->sw[i+1][j  ][k  ]                .     .
+ *  b2:                                     .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]                  .   .   .
+ *  b6:                                         .     .
+ *  b7: t->sw[i+1][j+1][k+1]                  .   .   .
+ *                                          O       . .
+ *                                O         .         O
+ *                                          .       .
+ *                                          .     .
+ *                                          .   .
+ *                                          . .
+ *                                          @
+ */
+static
+bool handle_case_0x744(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x744, i, j, k, i, jp1, k);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x744, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x750:                           O
+ *                                          . .
+ *  b0: t->sw[i  ][j  ][k  ]                .   .
+ *  b1: t->sw[i+1][j  ][k  ]                .     .
+ *  b2: t->sw[i  ][j+1][k  ]                .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                                     O         .
+ *  b5: t->sw[i+1][j  ][k+1]              .   .       .
+ *  b6:                                 .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]          .           .   .
+ *                                  .       O       . .
+ *                                O                   O
+ *                                  .               .
+ *                                    .           .
+ *                                      .       .
+ *                                        .   .
+ *                                          @
+ */
+static
+bool handle_case_0x750(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x750, i, j, k, i, j, kp1);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x750, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x788:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[ip1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .           .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .     .
+ *  b7:                           .       .   .       .
+ *                                .         O         .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x788(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[i][j][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x788, i, j, k, ip1, jp1, k);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x788, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7a0:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7:                           .   .   .       .
+ *                                . .       O       .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x7a0(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][j][k],
+					      t->sw[ip1][j][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7a0, i, j, k, ip1, j, kp1);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][kp1],
+					      t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7a0, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x7c0:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]              .   .   .   .
+ *  b6:                                 .       .     .
+ *  b7:                               .       .   .   .
+ *                                  .       O       . .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x7c0(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][j][kp1],
+					      t->sw[i][j][k],
+					      t->sw[i][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7c0, i, j, k, i, jp1, kp1);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[ip1][j][kp1],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][jp1][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x7c0, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * Handle the cases where a single corner is missing.
+ */
+
+/*
+ * 3D case 0x701:                           O
+ *                                        . . .
+ *  b0:                                     .   .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .   .   .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .   .   .   .   .
+ *                                . .       O       . .
+ *                                O                   O
+ *
+ *
+ *
+ *
+ *                                          @
+ */
+static
+bool handle_case_0x701(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+
+	if (install_tswitch(t, i, j, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[ip1][jp1][k],
+					      t->sw[ip1][j][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x701, i, j, k, i, j, k);
+	return false;
+}
+
+/*
+ * 3D case 0x702:                           O
+ *                                        . . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .   .
+ *  b1:                               .     .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .   .       .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .   .   .
+ *                                . .       O
+ *                                O         .         O
+ *                                  .       .
+ *                                    .     .
+ *                                      .   .
+ *                                        . .
+ *                                          @
+ */
+static
+bool handle_case_0x702(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x702, i, j, k, ip1, j, k);
+	return false;
+}
+
+/*
+ * 3D case 0x704:                           O
+ *                                        . . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .     .
+ *  b2:                             .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]        .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]          .       .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]            .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]              .   .   .   .
+ *                                          O       . .
+ *                                O         .         O
+ *                                          .       .
+ *                                          .     .
+ *                                          .   .
+ *                                          . .
+ *                                          @
+ */
+static
+bool handle_case_0x704(struct torus *t, int i, int j, int k)
+{
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, k,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[i][j][kp1],
+					      t->sw[i][jp1][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x704, i, j, k, i, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x708:                           O
+ *                                        .   .
+ *  b0: t->sw[i  ][j  ][k  ]            .       .
+ *  b1: t->sw[i+1][j  ][k  ]          .           .
+ *  b2: t->sw[i  ][j+1][k  ]        .               .
+ *  b3:                           O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .           .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .       .   .       .
+ *                                .         O         .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x708(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+
+	if (install_tswitch(t, ip1, jp1, k,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][j][k],
+					      t->sw[ip1][j][k]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x708, i, j, k, ip1, jp1, k);
+	return false;
+}
+
+/*
+ * 3D case 0x710:                           O
+ *                                        . . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4:                           .         O         .
+ *  b5: t->sw[i+1][j  ][k+1]      .       .   .       .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .           .   .
+ *                                . .       O       . .
+ *                                O                   O
+ *                                  .               .
+ *                                    .           .
+ *                                      .       .
+ *                                        .   .
+ *                                          @
+ */
+static
+bool handle_case_0x710(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, j, kp1,
+			    tfind_face_corner(t->sw[i][j][k],
+					      t->sw[ip1][j][k],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x710, i, j, k, i, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x720:                           O
+ *                                        . .
+ *  b0: t->sw[i  ][j  ][k  ]            .   .
+ *  b1: t->sw[i+1][j  ][k  ]          .     .
+ *  b2: t->sw[i  ][j+1][k  ]        .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O
+ *  b5:                           .   .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .
+ *  b7: t->sw[i+1][j+1][k+1]      .   .   .       .
+ *                                . .       O       .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x720(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, j, kp1,
+			    tfind_face_corner(t->sw[ip1][j][k],
+					      t->sw[i][j][k],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x720, i, j, k, ip1, j, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x740:                           O
+ *                                          . .
+ *  b0: t->sw[i  ][j  ][k  ]                .   .
+ *  b1: t->sw[i+1][j  ][k  ]                .     .
+ *  b2: t->sw[i  ][j+1][k  ]                .       .
+ *  b3: t->sw[i+1][j+1][k  ]      O         .         O
+ *  b4: t->sw[i  ][j  ][k+1]                O       . .
+ *  b5: t->sw[i+1][j  ][k+1]              .   .   .   .
+ *  b6:                                 .       .     .
+ *  b7: t->sw[i+1][j+1][k+1]          .       .   .   .
+ *                                  .       O       . .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x740(struct torus *t, int i, int j, int k)
+{
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, i, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][k],
+					      t->sw[i][j][k],
+					      t->sw[i][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x740, i, j, k, i, jp1, kp1);
+	return false;
+}
+
+/*
+ * 3D case 0x780:                           O
+ *
+ *  b0: t->sw[i  ][j  ][k  ]
+ *  b1: t->sw[i+1][j  ][k  ]
+ *  b2: t->sw[i  ][j+1][k  ]
+ *  b3: t->sw[i+1][j+1][k  ]      O                   O
+ *  b4: t->sw[i  ][j  ][k+1]      . .       O       . .
+ *  b5: t->sw[i+1][j  ][k+1]      .   .   .   .   .   .
+ *  b6: t->sw[i  ][j+1][k+1]      .     .       .     .
+ *  b7:                           .   .   .   .   .   .
+ *                                . .       O       . .
+ *                                O         .         O
+ *                                  .       .       .
+ *                                    .     .     .
+ *                                      .   .   .
+ *                                        . . .
+ *                                          @
+ */
+static
+bool handle_case_0x780(struct torus *t, int i, int j, int k)
+{
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	if (install_tswitch(t, ip1, jp1, kp1,
+			    tfind_face_corner(t->sw[i][jp1][kp1],
+					      t->sw[i][j][kp1],
+					      t->sw[ip1][j][kp1]))) {
+		return true;
+	}
+	log_no_crnr(t, 0x780, i, j, k, ip1, jp1, kp1);
+	return false;
+}
+
+/*
+ * Make sure links between all known torus/mesh switches are installed.
+ *
+ * We don't have to worry about links that wrap on a mesh coordinate, as
+ * there shouldn't be any; if there are it indicates an input error.
+ */
+static
+void check_tlinks(struct torus *t, int i, int j, int k)
+{
+	struct t_switch ****sw = t->sw;
+	int ip1 = canonicalize(i + 1, t->x_sz);
+	int jp1 = canonicalize(j + 1, t->y_sz);
+	int kp1 = canonicalize(k + 1, t->z_sz);
+
+	/*
+	 * Don't waste time/code checking return status of link_tswitches()
+	 * here.  It is unlikely to fail, and the result of any failure here
+	 * will be caught elsewhere anyway.
+	 */
+	if (sw[i][j][k] && sw[ip1][j][k])
+		link_tswitches(t, 0, sw[i][j][k], sw[ip1][j][k]);
+
+	if (sw[i][jp1][k] && sw[ip1][jp1][k])
+		link_tswitches(t, 0, sw[i][jp1][k], sw[ip1][jp1][k]);
+
+	if (sw[i][j][kp1] && sw[ip1][j][kp1])
+		link_tswitches(t, 0, sw[i][j][kp1], sw[ip1][j][kp1]);
+
+	if (sw[i][jp1][kp1] && sw[ip1][jp1][kp1])
+		link_tswitches(t, 0, sw[i][jp1][kp1], sw[ip1][jp1][kp1]);
+
+
+	if (sw[i][j][k] && sw[i][jp1][k])
+		link_tswitches(t, 1, sw[i][j][k], sw[i][jp1][k]);
+
+	if (sw[ip1][j][k] && sw[ip1][jp1][k])
+		link_tswitches(t, 1, sw[ip1][j][k], sw[ip1][jp1][k]);
+
+	if (sw[i][j][kp1] && sw[i][jp1][kp1])
+		link_tswitches(t, 1, sw[i][j][kp1], sw[i][jp1][kp1]);
+
+	if (sw[ip1][j][kp1] && sw[ip1][jp1][kp1])
+		link_tswitches(t, 1, sw[ip1][j][kp1], sw[ip1][jp1][kp1]);
+
+
+	if (sw[i][j][k] && sw[i][j][kp1])
+		link_tswitches(t, 2, sw[i][j][k], sw[i][j][kp1]);
+
+	if (sw[ip1][j][k] && sw[ip1][j][kp1])
+		link_tswitches(t, 2, sw[ip1][j][k], sw[ip1][j][kp1]);
+
+	if (sw[i][jp1][k] && sw[i][jp1][kp1])
+		link_tswitches(t, 2, sw[i][jp1][k], sw[i][jp1][kp1]);
+
+	if (sw[ip1][jp1][k] && sw[ip1][jp1][kp1])
+		link_tswitches(t, 2, sw[ip1][jp1][k], sw[ip1][jp1][kp1]);
+}
+
+static
+void locate_sw(struct torus *t, int i, int j, int k)
+{
+	unsigned fp;
+	bool success;
+
+	i = canonicalize(i, t->x_sz);
+	j = canonicalize(j, t->y_sz);
+	k = canonicalize(k, t->z_sz);
+
+	/*
+	 * By definition, if a coordinate direction is meshed, we don't
+	 * allow it to wrap to zero.
+	 */
+	if (t->flags & X_MESH) {
+		int ip1 = canonicalize(i + 1, t->x_sz);
+		if (ip1 < i)
+			goto out;
+	}
+	if (t->flags & Y_MESH) {
+		int jp1 = canonicalize(j + 1, t->y_sz);
+		if (jp1 < j)
+			goto out;
+	}
+	if (t->flags & Z_MESH) {
+		int kp1 = canonicalize(k + 1, t->z_sz);
+		if (kp1 < k)
+			goto out;
+	}
+	/*
+	 * There are various reasons that the links are not installed between
+	 * known torus switches.  These include cases where the search for
+	 * new switches only partially succeeds due to missing switches, and
+	 * cases where we haven't processed this position yet, but processing
+	 * of multiple independent neighbor positions has installed switches
+	 * into corners of our case.
+	 *
+	 * In any event, the topology assumptions made in handling the
+	 * fingerprint for this position require that all links be installed
+	 * between installed switches for this position.
+	 */
+again:
+	check_tlinks(t, i, j, k);
+	fp = fingerprint(t, i, j, k);
+
+	switch (fp) {
+	/*
+	 * When all switches are present, we are done.  Otherwise, one of
+	 * the cases below will be unsuccessful, and we'll be done also.
+	 *
+	 * Note that check_tlinks() above will ensure all links that are
+	 * present are connected, in the event that all our switches are
+	 * present due to successful case handling in the surrounding
+	 * torus/mesh.
+	 */
+	case 0x300:
+	case 0x500:
+	case 0x600:
+	case 0x700:
+		goto out;
+	/*
+	 * Ignore the 2D cases where there isn't enough information to uniquely
+	 * locate/place a switch into the cube.
+	 */
+	case 0x30f: 	/* 0 corners available */
+	case 0x533: 	/* 0 corners available */
+	case 0x655: 	/* 0 corners available */
+	case 0x30e:	/* 1 corner available */
+	case 0x532:	/* 1 corner available */
+	case 0x654:	/* 1 corner available */
+	case 0x30d:	/* 1 corner available */
+	case 0x531:	/* 1 corner available */
+	case 0x651:	/* 1 corner available */
+	case 0x30b:	/* 1 corner available */
+	case 0x523:	/* 1 corner available */
+	case 0x645:	/* 1 corner available */
+	case 0x307:	/* 1 corner available */
+	case 0x513:	/* 1 corner available */
+	case 0x615:	/* 1 corner available */
+		goto out;
+	/*
+	 * Handle the 2D cases with a single existing edge.
+	 *
+	 */
+	case 0x30c:
+		success = handle_case_0x30c(t, i, j, k);
+		break;
+	case 0x303:
+		success = handle_case_0x303(t, i, j, k);
+		break;
+	case 0x305:
+		success = handle_case_0x305(t, i, j, k);
+		break;
+	case 0x30a:
+		success = handle_case_0x30a(t, i, j, k);
+		break;
+	case 0x503:
+		success = handle_case_0x503(t, i, j, k);
+		break;
+	case 0x511:
+		success = handle_case_0x511(t, i, j, k);
+		break;
+	case 0x522:
+		success = handle_case_0x522(t, i, j, k);
+		break;
+	case 0x530:
+		success = handle_case_0x530(t, i, j, k);
+		break;
+	case 0x605:
+		success = handle_case_0x605(t, i, j, k);
+		break;
+	case 0x611:
+		success = handle_case_0x611(t, i, j, k);
+		break;
+	case 0x644:
+		success = handle_case_0x644(t, i, j, k);
+		break;
+	case 0x650:
+		success = handle_case_0x650(t, i, j, k);
+		break;
+	/*
+	 * Handle the 2D cases where two existing edges meet at a corner.
+	 */
+	case 0x301:
+		success = handle_case_0x301(t, i, j, k);
+		break;
+	case 0x302:
+		success = handle_case_0x302(t, i, j, k);
+		break;
+	case 0x304:
+		success = handle_case_0x304(t, i, j, k);
+		break;
+	case 0x308:
+		success = handle_case_0x308(t, i, j, k);
+		break;
+	case 0x501:
+		success = handle_case_0x501(t, i, j, k);
+		break;
+	case 0x502:
+		success = handle_case_0x502(t, i, j, k);
+		break;
+	case 0x520:
+		success = handle_case_0x520(t, i, j, k);
+		break;
+	case 0x510:
+		success = handle_case_0x510(t, i, j, k);
+		break;
+	case 0x601:
+		success = handle_case_0x601(t, i, j, k);
+		break;
+	case 0x604:
+		success = handle_case_0x604(t, i, j, k);
+		break;
+	case 0x610:
+		success = handle_case_0x610(t, i, j, k);
+		break;
+	case 0x640:
+		success = handle_case_0x640(t, i, j, k);
+		break;
+	/*
+	 * Ignore the 3D cases where there isn't enough information to uniquely
+	 * locate/place a switch into the cube.
+	 */
+	case 0x7ff:	/* 0 corners available */
+	case 0x7fe:	/* 1 corner available */
+	case 0x7fd:	/* 1 corner available */
+	case 0x7fb:	/* 1 corner available */
+	case 0x7f7:	/* 1 corner available */
+	case 0x7ef:	/* 1 corner available */
+	case 0x7df:	/* 1 corner available */
+	case 0x7bf:	/* 1 corner available */
+	case 0x77f:	/* 1 corner available */
+	case 0x7fc:	/* 2 adj corners available */
+	case 0x7fa:	/* 2 adj corners available */
+	case 0x7f5:	/* 2 adj corners available */
+	case 0x7f3:	/* 2 adj corners available */
+	case 0x7cf:	/* 2 adj corners available */
+	case 0x7af:	/* 2 adj corners available */
+	case 0x75f:	/* 2 adj corners available */
+	case 0x73f:	/* 2 adj corners available */
+	case 0x7ee:	/* 2 adj corners available */
+	case 0x7dd:	/* 2 adj corners available */
+	case 0x7bb:	/* 2 adj corners available */
+	case 0x777:	/* 2 adj corners available */
+		goto out;
+	/*
+	 * Handle the 3D cases where two existing edges meet at a corner.
+	 *
+	 */
+	case 0x71f:
+		success = handle_case_0x71f(t, i, j, k);
+		break;
+	case 0x72f:
+		success = handle_case_0x72f(t, i, j, k);
+		break;
+	case 0x737:
+		success = handle_case_0x737(t, i, j, k);
+		break;
+	case 0x73b:
+		success = handle_case_0x73b(t, i, j, k);
+		break;
+	case 0x74f:
+		success = handle_case_0x74f(t, i, j, k);
+		break;
+	case 0x757:
+		success = handle_case_0x757(t, i, j, k);
+		break;
+	case 0x75d:
+		success = handle_case_0x75d(t, i, j, k);
+		break;
+	case 0x773:
+		success = handle_case_0x773(t, i, j, k);
+		break;
+	case 0x775:
+		success = handle_case_0x775(t, i, j, k);
+		break;
+	case 0x78f:
+		success = handle_case_0x78f(t, i, j, k);
+		break;
+	case 0x7ab:
+		success = handle_case_0x7ab(t, i, j, k);
+		break;
+	case 0x7ae:
+		success = handle_case_0x7ae(t, i, j, k);
+		break;
+	case 0x7b3:
+		success = handle_case_0x7b3(t, i, j, k);
+		break;
+	case 0x7ba:
+		success = handle_case_0x7ba(t, i, j, k);
+		break;
+	case 0x7cd:
+		success = handle_case_0x7cd(t, i, j, k);
+		break;
+	case 0x7ce:
+		success = handle_case_0x7ce(t, i, j, k);
+		break;
+	case 0x7d5:
+		success = handle_case_0x7d5(t, i, j, k);
+		break;
+	case 0x7dc:
+		success = handle_case_0x7dc(t, i, j, k);
+		break;
+	case 0x7ea:
+		success = handle_case_0x7ea(t, i, j, k);
+		break;
+	case 0x7ec:
+		success = handle_case_0x7ec(t, i, j, k);
+		break;
+	case 0x7f1:
+		success = handle_case_0x7f1(t, i, j, k);
+		break;
+	case 0x7f2:
+		success = handle_case_0x7f2(t, i, j, k);
+		break;
+	case 0x7f4:
+		success = handle_case_0x7f4(t, i, j, k);
+		break;
+	case 0x7f8:
+		success = handle_case_0x7f8(t, i, j, k);
+		break;
+	/*
+	 * Handle the cases where three existing edges meet at a corner.
+	 *
+	 */
+	case 0x717:
+		success = handle_case_0x717(t, i, j, k);
+		break;
+	case 0x72b:
+		success = handle_case_0x72b(t, i, j, k);
+		break;
+	case 0x74d:
+		success = handle_case_0x74d(t, i, j, k);
+		break;
+	case 0x771:
+		success = handle_case_0x771(t, i, j, k);
+		break;
+	case 0x78e:
+		success = handle_case_0x78e(t, i, j, k);
+		break;
+	case 0x7b2:
+		success = handle_case_0x7b2(t, i, j, k);
+		break;
+	case 0x7d4:
+		success = handle_case_0x7d4(t, i, j, k);
+		break;
+	case 0x7e8:
+		success = handle_case_0x7e8(t, i, j, k);
+		break;
+	/*
+	 * Handle the cases where four corners on a single face are missing.
+	 */
+	case 0x70f:
+		success = handle_case_0x70f(t, i, j, k);
+		break;
+	case 0x733:
+		success = handle_case_0x733(t, i, j, k);
+		break;
+	case 0x755:
+		success = handle_case_0x755(t, i, j, k);
+		break;
+	case 0x7aa:
+		success = handle_case_0x7aa(t, i, j, k);
+		break;
+	case 0x7cc:
+		success = handle_case_0x7cc(t, i, j, k);
+		break;
+	case 0x7f0:
+		success = handle_case_0x7f0(t, i, j, k);
+		break;
+	/*
+	 * Handle the cases where three corners on a single face are missing.
+	 */
+	case 0x707:
+		success = handle_case_0x707(t, i, j, k);
+		break;
+	case 0x70b:
+		success = handle_case_0x70b(t, i, j, k);
+		break;
+	case 0x70d:
+		success = handle_case_0x70d(t, i, j, k);
+		break;
+	case 0x70e:
+		success = handle_case_0x70e(t, i, j, k);
+		break;
+	case 0x713:
+		success = handle_case_0x713(t, i, j, k);
+		break;
+	case 0x715:
+		success = handle_case_0x715(t, i, j, k);
+		break;
+	case 0x723:
+		success = handle_case_0x723(t, i, j, k);
+		break;
+	case 0x72a:
+		success = handle_case_0x72a(t, i, j, k);
+		break;
+	case 0x731:
+		success = handle_case_0x731(t, i, j, k);
+		break;
+	case 0x732:
+		success = handle_case_0x732(t, i, j, k);
+		break;
+	case 0x745:
+		success = handle_case_0x745(t, i, j, k);
+		break;
+	case 0x74c:
+		success = handle_case_0x74c(t, i, j, k);
+		break;
+	case 0x751:
+		success = handle_case_0x751(t, i, j, k);
+		break;
+	case 0x754:
+		success = handle_case_0x754(t, i, j, k);
+		break;
+	case 0x770:
+		success = handle_case_0x770(t, i, j, k);
+		break;
+	case 0x78a:
+		success = handle_case_0x78a(t, i, j, k);
+		break;
+	case 0x78c:
+		success = handle_case_0x78c(t, i, j, k);
+		break;
+	case 0x7a2:
+		success = handle_case_0x7a2(t, i, j, k);
+		break;
+	case 0x7a8:
+		success = handle_case_0x7a8(t, i, j, k);
+		break;
+	case 0x7b0:
+		success = handle_case_0x7b0(t, i, j, k);
+		break;
+	case 0x7c4:
+		success = handle_case_0x7c4(t, i, j, k);
+		break;
+	case 0x7c8:
+		success = handle_case_0x7c8(t, i, j, k);
+		break;
+	case 0x7d0:
+		success = handle_case_0x7d0(t, i, j, k);
+		break;
+	case 0x7e0:
+		success = handle_case_0x7e0(t, i, j, k);
+		break;
+	/*
+	 * Handle the cases where two corners on a single edge are missing.
+	 */
+	case 0x703:
+		success = handle_case_0x703(t, i, j, k);
+		break;
+	case 0x705:
+		success = handle_case_0x705(t, i, j, k);
+		break;
+	case 0x70a:
+		success = handle_case_0x70a(t, i, j, k);
+		break;
+	case 0x70c:
+		success = handle_case_0x70c(t, i, j, k);
+		break;
+	case 0x711:
+		success = handle_case_0x711(t, i, j, k);
+		break;
+	case 0x722:
+		success = handle_case_0x722(t, i, j, k);
+		break;
+	case 0x730:
+		success = handle_case_0x730(t, i, j, k);
+		break;
+	case 0x744:
+		success = handle_case_0x744(t, i, j, k);
+		break;
+	case 0x750:
+		success = handle_case_0x750(t, i, j, k);
+		break;
+	case 0x788:
+		success = handle_case_0x788(t, i, j, k);
+		break;
+	case 0x7a0:
+		success = handle_case_0x7a0(t, i, j, k);
+		break;
+	case 0x7c0:
+		success = handle_case_0x7c0(t, i, j, k);
+		break;
+	/*
+	 * Handle the cases where a single corner is missing.
+	 */
+	case 0x701:
+		success = handle_case_0x701(t, i, j, k);
+		break;
+	case 0x702:
+		success = handle_case_0x702(t, i, j, k);
+		break;
+	case 0x704:
+		success = handle_case_0x704(t, i, j, k);
+		break;
+	case 0x708:
+		success = handle_case_0x708(t, i, j, k);
+		break;
+	case 0x710:
+		success = handle_case_0x710(t, i, j, k);
+		break;
+	case 0x720:
+		success = handle_case_0x720(t, i, j, k);
+		break;
+	case 0x740:
+		success = handle_case_0x740(t, i, j, k);
+		break;
+	case 0x780:
+		success = handle_case_0x780(t, i, j, k);
+		break;
+
+	default:
+		/*
+		 * There's lots of unhandled cases still, but it's not clear
+		 * we care.  Let debugging show us what they are so we can
+		 * learn if we care.
+		 */
+		if (t->debug)
+			OSM_LOG(&t->osm->log, OSM_LOG_ERROR,
+				"Unhandled fingerprint 0x%03x @ %d %d %d\n",
+				fp, i, j, k);
+		goto out;
+	}
+	/*
+	 * If we successfully handled a case, we may be able to make more
+	 * progress at this position, so try again.  Otherwise, even though
+	 * we didn't successfully handle a case, we may have installed a
+	 * switch into the torus/mesh, so try to install links as well.
+	 * Then we'll have another go at the next position.
+	 */
+	if (success) {
+		if (t->debug)
+			OSM_LOG(&t->osm->log, OSM_LOG_ERROR,
+				"Success on fingerprint 0x%03x @ %d %d %d\n",
+				fp, i, j, k);
+		goto again;
+	} else {
+		check_tlinks(t, i, j, k);
+		if (t->debug)
+			OSM_LOG(&t->osm->log, OSM_LOG_ERROR,
+				"Failed on fingerprint 0x%03x @ %d %d %d\n",
+				fp, i, j, k);
+	}
+out:
+	return;
+}
