diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_diagramme_class.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_diagramme_class.fig
index 6d1cf3be46d..a236cfaeae3 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_diagramme_class.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_diagramme_class.fig
@@ -32,7 +32,7 @@ Single
 4 0 0 40 -1 1 11 0.0000 4 150 645 11888 5065 d, GMap\001
 4 0 0 50 -1 2 14 0.0000 4 210 2595 9586 5781 - Dart_handle alpha[d+1]\001
 4 0 0 50 -1 2 14 0.0000 4 195 3015 9586 6037 - Attribute_handles attributes\001
-4 0 0 50 -1 2 18 0.0000 4 210 855 10660 5372 GDart\001
+4 0 0 50 -1 2 18 0.0000 4 270 1545 10224 5365 GMap_dart\001
 -6
 6 3600 7009 7795 8544
 6 6618 7009 7795 7316
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_3d_sew.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_3d_sew.fig
index 5588c2d7ee0..d10a4fb1396 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_3d_sew.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_3d_sew.fig
@@ -201,6 +201,7 @@ Single
 1 3 0 0 39 39 25 -1 20 0.000 1 0.0000 3234 1381 64 64 3234 1381 3275 1430
 1 3 0 0 39 39 25 -1 20 0.000 1 0.0000 3153 3149 64 64 3153 3149 3194 3198
 1 3 0 0 39 39 25 -1 20 0.000 1 0.0000 3250 3254 64 64 3250 3254 3291 3303
+1 3 0 0 39 39 25 -1 20 0.000 1 0.0000 405 2565 64 64 405 2565 446 2614
 2 1 0 1 33 35 45 -1 -1 0.000 0 0 -1 0 0 2
 	 1349 766 1209 1048
 2 1 0 1 33 35 45 -1 -1 0.000 0 0 -1 0 0 2
@@ -595,5 +596,5 @@ Single
 4 0 0 50 -1 0 16 0.0000 4 180 135 9182 2492 g\001
 4 0 0 50 -1 0 16 0.0000 4 180 135 9211 1831 h\001
 -6
-4 0 0 50 -1 0 18 0.0000 4 255 1530 4770 -90 sew<3>(1,a)\001
-4 0 0 50 -1 0 18 0.0000 4 255 1620 5175 3375 unsew<3>(1)\001
+4 0 0 50 -1 0 18 0.0000 4 255 1995 4770 -90 gm.sew<3>(1,a)\001
+4 0 0 50 -1 0 18 0.0000 4 255 2085 5175 3375 gm.unsew<3>(1)\001
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_insertions.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_insertions.fig
index f365de650e3..e8dd48a3743 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_insertions.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_example_insertions.fig
@@ -45,7 +45,7 @@ Single
 2 1 0 1 34 0 614 0 -1 0.000 1 0 7 0 0 2
 	 4059 10293 3227 8862
 -6
-6 3264 6873 6508 9564
+6 3264 6873 6493 9549
 2 1 0 1 35 0 819 0 -1 0.000 1 0 7 0 0 2
 	 5921 9026 5927 8860
 2 1 0 1 35 0 350 0 -1 0.000 1 0 7 0 0 2
@@ -54,10 +54,12 @@ Single
 	 3279 6888 5435 8257
 2 1 0 2 33 0 796 0 -1 0.000 1 0 7 0 0 2
 	 5435 8257 6478 9534
-2 1 0 4 33 0 298 0 -1 0.000 1 0 7 0 0 2
-	 6478 9534 4204 8194
 2 1 0 2 33 0 747 0 -1 0.000 1 0 7 0 0 2
 	 4204 8194 3279 6888
+2 1 0 4 33 0 298 -1 -1 0.000 1 0 -1 0 0 2
+	 4217 8199 5446 8932
+2 1 0 2 33 0 298 0 -1 0.000 1 0 7 0 0 2
+	 6478 9534 4204 8194
 -6
 6 3442 8420 6465 10397
 2 1 0 1 35 0 535 0 -1 0.000 1 0 7 0 0 2
@@ -198,10 +200,12 @@ Single
 	 -6263 6598 -6226 6710
 2 1 0 1 35 0 860 0 -1 0.000 1 0 7 0 0 2
 	 -7555 7698 -7306 7620
-2 1 0 3 33 0 872 0 -1 0.000 1 0 7 0 0 2
-	 -7333 6623 -7278 8553
 2 1 0 1 33 0 703 0 -1 0.000 1 0 7 0 0 2
 	 -5186 8755 -5096 6797
+2 1 0 3 33 0 872 -1 -1 0.000 1 0 -1 0 0 2
+	 -7333 6625 -7307 7623
+2 1 0 1 33 0 872 0 -1 0.000 1 0 7 0 0 2
+	 -7333 6623 -7278 8553
 -6
 6 -8214 6695 -7520 9847
 2 1 0 1 35 0 762 0 -1 0.000 1 0 7 0 0 2
@@ -247,17 +251,19 @@ Single
 2 1 0 1 34 0 670 0 -1 0.000 1 0 7 0 0 2
 	 -5480 10194 -5218 9034
 -6
-6 -8059 7865 -5220 10271
+6 -8063 7871 -5220 10271
 2 1 0 1 33 0 176 0 -1 0.000 1 0 7 0 0 2
 	 -5452 8114 -5530 10271
 2 1 0 1 35 0 206 0 -1 0.000 1 0 7 0 0 2
 	 -5220 9129 -5492 9234
 2 1 0 1 33 0 403 0 -1 0.000 1 0 7 0 0 2
 	 -5530 10271 -7927 10002
-2 1 0 3 33 0 872 0 -1 0.000 1 0 7 0 0 2
-	 -7927 10002 -8044 7880
 2 1 0 1 33 0 403 0 -1 0.000 1 0 7 0 0 2
 	 -8044 7880 -5452 8114
+2 1 0 3 33 0 872 -1 -1 0.000 1 0 -1 0 0 2
+	 -8048 7886 -7984 8987
+2 1 0 1 33 0 403 0 -1 0.000 1 0 7 0 0 2
+	 -7927 10002 -8044 7880
 -6
 6 -5268 6907 -4899 10159
 2 1 0 1 34 0 740 0 -1 0.000 1 0 7 0 0 2
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_facet.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_facet.fig
index 2926f1efa16..92c8a8ab04d 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_facet.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_facet.fig
@@ -119,7 +119,7 @@ Single
 	 3029 2405 3117 619
 -6
 -6
-6 6119 963 9579 4564
+6 6119 966 9579 4564
 6 6196 966 8346 2865
 2 1 0 1 35 0 924 0 -1 0.000 1 0 7 0 0 2
 	 7520 2795 7375 2589
@@ -150,7 +150,7 @@ Single
 2 1 0 1 33 0 614 0 -1 0.000 1 0 7 0 0 2
 	 7119 4398 6287 2967
 -6
-6 6309 963 9553 3654
+6 6324 978 9553 3654
 2 1 0 1 35 0 819 0 -1 0.000 1 0 7 0 0 2
 	 8981 3131 8987 2965
 2 1 0 1 35 0 350 0 -1 0.000 1 0 7 0 0 2
@@ -161,7 +161,9 @@ Single
 	 6339 993 8495 2362
 2 1 0 2 32 0 796 0 -1 0.000 1 0 7 0 0 2
 	 8495 2362 9538 3639
-2 1 0 4 32 0 298 0 -1 0.000 1 0 7 0 0 2
+2 1 0 4 32 0 298 -1 -1 0.000 1 0 -1 0 0 2
+	 6753 1576 7260 2292
+2 1 0 2 32 0 298 0 -1 0.000 1 0 7 0 0 2
 	 7264 2299 6339 993
 -6
 6 6502 2525 9525 4502
@@ -309,11 +311,15 @@ Single
 1 3 0 0 37 37 25 -1 20 0.000 1 0.0000 7533 2083 64 64 7533 2083 7574 2132
 1 3 0 0 37 37 25 -1 20 0.000 1 0.0000 7571 1831 64 64 7571 1831 7612 1880
 1 3 0 0 37 37 25 -1 20 0.000 1 0.0000 7801 2091 64 64 7801 2091 7842 2140
-4 0 0 50 -1 0 18 0.0000 4 255 3525 3831 281 (std::vector{dh1,dh2,dh3,dh4})\001
-4 0 0 50 -1 0 18 0.0000 4 255 3600 2113 -50 dh5=gm.insert_cell_2_in_cell_3\001
-4 0 0 50 -1 0 20 0.0000 4 225 495 1884 2971 dh1\001
-4 0 0 50 -1 0 20 0.0000 4 225 495 1704 1051 dh3\001
-4 0 0 50 -1 0 20 0.0000 4 225 495 161 831 dh2\001
-4 0 0 50 -1 0 20 0.0000 4 225 495 3093 3194 dh4\001
-4 0 0 50 -1 0 20 0.0000 4 240 495 6336 1929 dh5\001
-4 0 0 50 -1 0 18 0.0000 4 255 2730 3081 4380 gm.remove_cell<2>(d5)\001
+4 0 0 50 -1 0 18 0.0000 4 270 3960 2113 -50 dh9=gm.insert_cell_2_in_cell_3\001
+4 0 0 50 -1 0 18 0.0000 4 270 3120 3468 4305 gm.remove_cell<2>(dh9)\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 2005 3054 dh1\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 1055 2134 dh2\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 83 1157 dh3\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 191 808 dh4\001
+4 0 0 50 -1 0 18 0.0000 4 270 3090 3831 281 (std::vector{dh1,...,dh8})\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 1511 887 dh5\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 2391 1728 dh6\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 3110 2978 dh7\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 3003 3493 dh8\001
+4 0 0 50 -1 0 18 0.0000 4 210 450 6544 2153 dh9\001
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_vertex.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_vertex.fig
index 0536a7baf64..b55c80449ba 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_vertex.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_insert_vertex.fig
@@ -420,5 +420,5 @@ Single
 2 1 0 4 32 0 365 -1 -1 0.000 1 0 -1 0 0 2
 	 2029 1306 2492 895
 4 0 0 50 -1 0 18 0.0000 4 270 4620 3264 172 dh2=gm.insert_cell_0_in_cell_1(dh1)\001
-4 0 0 50 -1 0 18 0.0000 4 270 3120 3743 4339 gm.remove_cell<0>(dh2)\001
 4 0 0 50 -1 0 15 0.0000 4 180 405 1947 1039 dh1\001
+4 0 0 50 -1 0 18 0.0000 4 270 3120 3896 4296 gm.remove_cell<0>(dh2)\001
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_non_valid.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_non_valid.fig
index 63d176170f0..a147cb7c5f1 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_non_valid.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_non_valid.fig
@@ -41,7 +41,7 @@ Single
 0 63 #828282
 0 64 #676767
 0 65 #5d5d5d
-6 -5535 405 -495 3645
+6 -5520 439 -534 3612
 6 -2709 939 -577 3548
 6 -2520 2646 -594 3548
 2 1 0 2 32 0 635 0 -1 0.000 1 0 7 0 0 2
@@ -203,6 +203,7 @@ Single
 1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 -613 2695 64 64 -613 2695 -572 2744
 1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 -620 2481 64 64 -620 2481 -579 2530
 1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 -598 2383 64 64 -598 2383 -557 2432
+1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 -2376 1600 64 64 -2376 1600 -2335 1649
 2 1 0 2 58 56 45 -1 -1 0.000 0 0 -1 0 0 2
 	 -4264 1215 -4396 1480
 2 1 0 2 58 56 45 -1 -1 0.000 0 0 -1 0 0 2
@@ -254,7 +255,7 @@ Single
 4 0 0 50 -1 0 18 0.0000 4 210 150 -2805 2287 h\001
 4 0 0 50 -1 0 18 0.0000 4 195 150 -2840 1960 4\001
 -6
-6 315 360 5355 3600
+6 330 394 5316 3567
 6 3141 894 5273 3503
 6 3330 2601 5256 3503
 2 1 0 2 32 0 635 0 -1 0.000 1 0 7 0 0 2
@@ -416,6 +417,7 @@ Single
 1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 5237 2650 64 64 5237 2650 5278 2699
 1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 5230 2436 64 64 5230 2436 5271 2485
 1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 5252 2338 64 64 5252 2338 5293 2387
+1 3 0 0 65 65 25 -1 20 0.000 1 0.0000 3477 1551 64 64 3477 1551 3518 1600
 2 1 0 2 58 56 45 -1 -1 0.000 0 0 -1 0 0 2
 	 1586 1170 1454 1435
 2 1 0 2 58 56 45 -1 -1 0.000 0 0 -1 0 0 2
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_triangulation.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_triangulation.fig
index 369ddcbdcf9..d1bb7917d82 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_triangulation.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_triangulation.fig
@@ -221,18 +221,20 @@ Single
 2 1 0 2 35 0 712 0 -1 0.000 1 0 7 0 0 2
 	 1989 3100 2598 2029
 -6
-6 4124 832 4819 3674
-2 1 0 4 36 0 206 0 -1 0.000 1 0 7 0 0 2
-	 4154 3644 4453 1940
+6 4127 832 4819 3659
 2 1 0 2 35 0 610 0 -1 0.000 1 0 7 0 0 2
 	 4804 847 4507 2442
 2 1 0 2 35 0 245 0 -1 0.000 1 0 7 0 0 2
 	 4453 1940 4804 847
 2 1 0 2 35 0 571 0 -1 0.000 1 0 7 0 0 2
 	 4507 2442 4154 3644
+2 1 0 4 36 0 206 -1 -1 0.000 1 0 -1 0 0 2
+	 4157 3629 4308 2780
+2 1 0 2 35 0 207 0 -1 0.000 1 0 7 0 0 2
+	 4154 3644 4453 1940
 -6
 -6
-6 -394 47 2468 3099
+6 -394 47 2477 3099
 6 -311 47 2341 1261
 2 1 0 1 32 0 691 0 -1 0.000 1 0 7 0 0 2
 	 638 47 2341 332
@@ -283,20 +285,22 @@ Single
 2 1 0 1 32 0 723 0 -1 0.000 1 0 7 0 0 2
 	 2373 383 691 99
 -6
-6 1713 414 2468 3058
+6 1713 426 2477 3058
 2 1 0 2 35 0 409 0 -1 0.000 1 0 7 0 0 2
 	 1765 3043 1728 1389
 2 1 0 2 35 0 726 0 -1 0.000 1 0 7 0 0 2
 	 2398 1986 1765 3043
-2 1 0 4 36 0 760 0 -1 0.000 1 0 7 0 0 2
-	 2438 444 2398 1986
 2 1 0 2 35 0 443 0 -1 0.000 1 0 7 0 0 2
 	 1728 1389 2438 444
+2 1 0 2 35 0 709 0 -1 0.000 1 0 7 0 0 2
+	 2438 444 2398 1986
+2 1 0 4 36 0 708 -1 -1 0.000 1 0 -1 0 0 2
+	 2447 456 2421 1282
 -6
 -6
 -6
 6 5537 569 10528 3655
-6 5537 569 8350 3152
+6 5537 569 8337 3152
 6 5537 655 6705 2704
 2 1 0 1 32 0 857 0 -1 0.000 1 0 7 0 0 2
 	 5671 2704 6705 2232
@@ -337,13 +341,15 @@ Single
 2 1 0 1 32 0 949 0 -1 0.000 1 0 7 0 0 2
 	 6773 649 6827 2222
 -6
-6 7859 763 8350 2504
-2 1 0 4 36 0 680 0 -1 0.000 1 0 7 0 0 2
-	 7889 1868 8320 793
+6 7874 774 8337 2504
 2 1 0 2 35 0 738 0 -1 0.000 1 0 7 0 0 2
 	 8292 2489 7889 1868
 2 1 0 2 35 0 787 0 -1 0.000 1 0 7 0 0 2
 	 8320 793 8292 2489
+2 1 0 4 36 0 680 -1 -1 0.000 1 0 -1 0 0 2
+	 8307 804 8095 1358
+2 1 0 2 35 0 681 0 -1 0.000 1 0 7 0 0 2
+	 7889 1868 8320 793
 -6
 6 7364 1937 8278 3152
 2 1 0 2 35 0 678 0 -1 0.000 1 0 7 0 0 2
@@ -461,12 +467,14 @@ Single
 2 1 0 2 35 0 182 0 -1 0.000 1 0 7 0 0 2
 	 10126 2145 9862 1302
 -6
-6 9650 1392 10127 3630
+6 9656 1392 10112 3624
 2 1 0 2 35 0 172 0 -1 0.000 1 0 7 0 0 2
 	 9828 1407 10097 2240
 2 1 0 2 35 0 104 0 -1 0.000 1 0 7 0 0 2
 	 9680 3600 9828 1407
-2 1 0 4 36 0 276 0 -1 0.000 1 0 7 0 0 2
+2 1 0 4 36 0 276 -1 -1 0.000 1 0 -1 0 0 2
+	 9686 3594 9900 2888
+2 1 0 2 35 0 277 0 -1 0.000 1 0 7 0 0 2
 	 10097 2240 9680 3600
 -6
 6 10129 975 10528 2864
@@ -604,6 +612,9 @@ Single
 1 3 0 0 189 189 25 -1 20 0.000 1 0.0000 10107 2101 64 64 10107 2101 10148 2150
 1 3 0 0 189 189 25 -1 20 0.000 1 0.0000 10175 2200 64 64 10175 2200 10216 2249
 1 3 0 0 189 189 25 -1 20 0.000 1 0.0000 10135 2382 64 64 10135 2382 10176 2431
+1 3 0 0 189 189 25 -1 20 0.000 1 0.0000 1976 1430 64 64 1976 1430 2017 1479
+1 3 0 0 189 189 25 -1 20 0.000 1 0.0000 2154 1351 64 64 2154 1351 2195 1400
+1 3 0 0 189 189 25 -1 20 0.000 1 0.0000 2081 1543 64 64 2081 1543 2122 1592
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
 	 5 532 217 496
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
@@ -647,13 +658,11 @@ Single
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
 	 3138 3408 3006 3496
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
-	 4074 2782 4365 2852
+	 4074 2782 4365 2793
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
 	 4471 1273 4647 1511
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
 	 4524 1696 4691 1776
-2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
-	 4180 3046 4418 2976
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
 	 6173 644 6147 804
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
@@ -724,8 +733,10 @@ Single
 	 10223 1599 10337 1723
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
 	 10280 2494 10176 2639
+2 1 0 2 54 34 450 -1 -1 0.000 0 0 -1 0 0 2
+	 4180 3046 4418 2976
 2 1 0 2 54 34 45 -1 -1 0.000 0 0 -1 0 0 2
-	 9845 2794 10057 2867
+	 9849 2864 10056 2927
 4 0 0 50 -1 0 18 0.0000 4 270 7350 4353 4232 Vector<Dart_handle>v2 = {Dart_of_cell_range<0,2>(dh4)}\001
 4 0 0 50 -1 -1 18 0.0000 4 270 4470 4790 4526 a in v1 U v2: gm.remove_cell<1>(a)\001
 4 0 0 50 -1 0 18 0.0000 4 270 4620 4161 175 dh4=gm.insert_cell_0_in_cell_2(dh2)\001
diff --git a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_with_attribs.fig b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_with_attribs.fig
index b6410a37ca2..67e81b04eb8 100644
--- a/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_with_attribs.fig
+++ b/Generalized_map/doc/Generalized_map/fig/fig_src/gmap_with_attribs.fig
@@ -36,7 +36,7 @@ Single
 0 58 #9f9f9f
 0 59 #535353
 0 60 #5d5d5d
-0 61 #676767
+0 61 #000000
 0 62 #343434
 6 180 360 5220 3915
 6 3690 1591 4446 1849
@@ -327,7 +327,7 @@ Single
 4 0 0 50 -1 0 16 0.0000 4 180 135 2612 2942 g\001
 4 0 0 50 -1 0 16 0.0000 4 180 135 2641 2281 h\001
 -6
-6 -5355 450 -1350 3825
+6 -5354 482 -1350 3782
 6 -4446 1299 -3550 1569
 2 2 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
 	 -4431 1314 -3565 1314 -3565 1554 -4431 1554 -4431 1314