Take as first grid (in levels 1, 2, 3, 7, 8 and 9) 6x special composite 12x12 magic square and (in levels 4, 5, 6, 10, 11 and 12) 6x its inverse. The second grid consists of the numbers 0 up to 11. See below the result.
12x12x12 pantriagonal magic cube
1 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 6 | 1 | 8 | 1651 | 1656 | 1649 | 114 | 109 | 116 | 1687 | 1692 | 1685 | |
10374 | 7 | 5 | 3 | 1650 | 1652 | 1654 | 115 | 113 | 111 | 1686 | 1688 | 1690 | |
10374 | 2 | 9 | 4 | 1655 | 1648 | 1653 | 110 | 117 | 112 | 1691 | 1684 | 1689 | |
10374 | 1705 | 1710 | 1703 | 96 | 91 | 98 | 1597 | 1602 | 1595 | 60 | 55 | 62 | |
10374 | 1704 | 1706 | 1708 | 97 | 95 | 93 | 1596 | 1598 | 1600 | 61 | 59 | 57 | |
10374 | 1709 | 1702 | 1707 | 92 | 99 | 94 | 1601 | 1594 | 1599 | 56 | 63 | 58 | |
10374 | 31 | 36 | 29 | 1626 | 1621 | 1628 | 139 | 144 | 137 | 1662 | 1657 | 1664 | |
10374 | 30 | 32 | 34 | 1627 | 1625 | 1623 | 138 | 140 | 142 | 1663 | 1661 | 1659 | |
10374 | 35 | 28 | 33 | 1622 | 1629 | 1624 | 143 | 136 | 141 | 1658 | 1665 | 1660 | |
10374 | 1716 | 1711 | 1718 | 85 | 90 | 83 | 1608 | 1603 | 1610 | 49 | 54 | 47 | |
10374 | 1717 | 1715 | 1713 | 84 | 86 | 88 | 1609 | 1607 | 1605 | 48 | 50 | 52 | |
10374 | 1712 | 1719 | 1714 | 89 | 82 | 87 | 1604 | 1611 | 1606 | 53 | 46 | 51 | |
2 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 150 | 145 | 152 | 1507 | 1512 | 1505 | 258 | 253 | 260 | 1543 | 1548 | 1541 | |
10374 | 151 | 149 | 147 | 1506 | 1508 | 1510 | 259 | 257 | 255 | 1542 | 1544 | 1546 | |
10374 | 146 | 153 | 148 | 1511 | 1504 | 1509 | 254 | 261 | 256 | 1547 | 1540 | 1545 | |
10374 | 1561 | 1566 | 1559 | 240 | 235 | 242 | 1453 | 1458 | 1451 | 204 | 199 | 206 | |
10374 | 1560 | 1562 | 1564 | 241 | 239 | 237 | 1452 | 1454 | 1456 | 205 | 203 | 201 | |
10374 | 1565 | 1558 | 1563 | 236 | 243 | 238 | 1457 | 1450 | 1455 | 200 | 207 | 202 | |
10374 | 175 | 180 | 173 | 1482 | 1477 | 1484 | 283 | 288 | 281 | 1518 | 1513 | 1520 | |
10374 | 174 | 176 | 178 | 1483 | 1481 | 1479 | 282 | 284 | 286 | 1519 | 1517 | 1515 | |
10374 | 179 | 172 | 177 | 1478 | 1485 | 1480 | 287 | 280 | 285 | 1514 | 1521 | 1516 | |
10374 | 1572 | 1567 | 1574 | 229 | 234 | 227 | 1464 | 1459 | 1466 | 193 | 198 | 191 | |
10374 | 1573 | 1571 | 1569 | 228 | 230 | 232 | 1465 | 1463 | 1461 | 192 | 194 | 196 | |
10374 | 1568 | 1575 | 1570 | 233 | 226 | 231 | 1460 | 1467 | 1462 | 197 | 190 | 195 | |
3 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 294 | 289 | 296 | 1363 | 1368 | 1361 | 402 | 397 | 404 | 1399 | 1404 | 1397 | |
10374 | 295 | 293 | 291 | 1362 | 1364 | 1366 | 403 | 401 | 399 | 1398 | 1400 | 1402 | |
10374 | 290 | 297 | 292 | 1367 | 1360 | 1365 | 398 | 405 | 400 | 1403 | 1396 | 1401 | |
10374 | 1417 | 1422 | 1415 | 384 | 379 | 386 | 1309 | 1314 | 1307 | 348 | 343 | 350 | |
10374 | 1416 | 1418 | 1420 | 385 | 383 | 381 | 1308 | 1310 | 1312 | 349 | 347 | 345 | |
10374 | 1421 | 1414 | 1419 | 380 | 387 | 382 | 1313 | 1306 | 1311 | 344 | 351 | 346 | |
10374 | 319 | 324 | 317 | 1338 | 1333 | 1340 | 427 | 432 | 425 | 1374 | 1369 | 1376 | |
10374 | 318 | 320 | 322 | 1339 | 1337 | 1335 | 426 | 428 | 430 | 1375 | 1373 | 1371 | |
10374 | 323 | 316 | 321 | 1334 | 1341 | 1336 | 431 | 424 | 429 | 1370 | 1377 | 1372 | |
10374 | 1428 | 1423 | 1430 | 373 | 378 | 371 | 1320 | 1315 | 1322 | 337 | 342 | 335 | |
10374 | 1429 | 1427 | 1425 | 372 | 374 | 376 | 1321 | 1319 | 1317 | 336 | 338 | 340 | |
10374 | 1424 | 1431 | 1426 | 377 | 370 | 375 | 1316 | 1323 | 1318 | 341 | 334 | 339 | |
4 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 571 | 576 | 569 | 1230 | 1225 | 1232 | 463 | 468 | 461 | 1194 | 1189 | 1196 | |
10374 | 570 | 572 | 574 | 1231 | 1229 | 1227 | 462 | 464 | 466 | 1195 | 1193 | 1191 | |
10374 | 575 | 568 | 573 | 1226 | 1233 | 1228 | 467 | 460 | 465 | 1190 | 1197 | 1192 | |
10374 | 1176 | 1171 | 1178 | 481 | 486 | 479 | 1284 | 1279 | 1286 | 517 | 522 | 515 | |
10374 | 1177 | 1175 | 1173 | 480 | 482 | 484 | 1285 | 1283 | 1281 | 516 | 518 | 520 | |
10374 | 1172 | 1179 | 1174 | 485 | 478 | 483 | 1280 | 1287 | 1282 | 521 | 514 | 519 | |
10374 | 546 | 541 | 548 | 1255 | 1260 | 1253 | 438 | 433 | 440 | 1219 | 1224 | 1217 | |
10374 | 547 | 545 | 543 | 1254 | 1256 | 1258 | 439 | 437 | 435 | 1218 | 1220 | 1222 | |
10374 | 542 | 549 | 544 | 1259 | 1252 | 1257 | 434 | 441 | 436 | 1223 | 1216 | 1221 | |
10374 | 1165 | 1170 | 1163 | 492 | 487 | 494 | 1273 | 1278 | 1271 | 528 | 523 | 530 | |
10374 | 1164 | 1166 | 1168 | 493 | 491 | 489 | 1272 | 1274 | 1276 | 529 | 527 | 525 | |
10374 | 1169 | 1162 | 1167 | 488 | 495 | 490 | 1277 | 1270 | 1275 | 524 | 531 | 526 | |
5 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 715 | 720 | 713 | 1086 | 1081 | 1088 | 607 | 612 | 605 | 1050 | 1045 | 1052 | |
10374 | 714 | 716 | 718 | 1087 | 1085 | 1083 | 606 | 608 | 610 | 1051 | 1049 | 1047 | |
10374 | 719 | 712 | 717 | 1082 | 1089 | 1084 | 611 | 604 | 609 | 1046 | 1053 | 1048 | |
10374 | 1032 | 1027 | 1034 | 625 | 630 | 623 | 1140 | 1135 | 1142 | 661 | 666 | 659 | |
10374 | 1033 | 1031 | 1029 | 624 | 626 | 628 | 1141 | 1139 | 1137 | 660 | 662 | 664 | |
10374 | 1028 | 1035 | 1030 | 629 | 622 | 627 | 1136 | 1143 | 1138 | 665 | 658 | 663 | |
10374 | 690 | 685 | 692 | 1111 | 1116 | 1109 | 582 | 577 | 584 | 1075 | 1080 | 1073 | |
10374 | 691 | 689 | 687 | 1110 | 1112 | 1114 | 583 | 581 | 579 | 1074 | 1076 | 1078 | |
10374 | 686 | 693 | 688 | 1115 | 1108 | 1113 | 578 | 585 | 580 | 1079 | 1072 | 1077 | |
10374 | 1021 | 1026 | 1019 | 636 | 631 | 638 | 1129 | 1134 | 1127 | 672 | 667 | 674 | |
10374 | 1020 | 1022 | 1024 | 637 | 635 | 633 | 1128 | 1130 | 1132 | 673 | 671 | 669 | |
10374 | 1025 | 1018 | 1023 | 632 | 639 | 634 | 1133 | 1126 | 1131 | 668 | 675 | 670 | |
6 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 859 | 864 | 857 | 942 | 937 | 944 | 751 | 756 | 749 | 906 | 901 | 908 | |
10374 | 858 | 860 | 862 | 943 | 941 | 939 | 750 | 752 | 754 | 907 | 905 | 903 | |
10374 | 863 | 856 | 861 | 938 | 945 | 940 | 755 | 748 | 753 | 902 | 909 | 904 | |
10374 | 888 | 883 | 890 | 769 | 774 | 767 | 996 | 991 | 998 | 805 | 810 | 803 | |
10374 | 889 | 887 | 885 | 768 | 770 | 772 | 997 | 995 | 993 | 804 | 806 | 808 | |
10374 | 884 | 891 | 886 | 773 | 766 | 771 | 992 | 999 | 994 | 809 | 802 | 807 | |
10374 | 834 | 829 | 836 | 967 | 972 | 965 | 726 | 721 | 728 | 931 | 936 | 929 | |
10374 | 835 | 833 | 831 | 966 | 968 | 970 | 727 | 725 | 723 | 930 | 932 | 934 | |
10374 | 830 | 837 | 832 | 971 | 964 | 969 | 722 | 729 | 724 | 935 | 928 | 933 | |
10374 | 877 | 882 | 875 | 780 | 775 | 782 | 985 | 990 | 983 | 816 | 811 | 818 | |
10374 | 876 | 878 | 880 | 781 | 779 | 777 | 984 | 986 | 988 | 817 | 815 | 813 | |
10374 | 881 | 874 | 879 | 776 | 783 | 778 | 989 | 982 | 987 | 812 | 819 | 814 | |
7 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 1590 | 1585 | 1592 | 67 | 72 | 65 | 1698 | 1693 | 1700 | 103 | 108 | 101 | |
10374 | 1591 | 1589 | 1587 | 66 | 68 | 70 | 1699 | 1697 | 1695 | 102 | 104 | 106 | |
10374 | 1586 | 1593 | 1588 | 71 | 64 | 69 | 1694 | 1701 | 1696 | 107 | 100 | 105 | |
10374 | 121 | 126 | 119 | 1680 | 1675 | 1682 | 13 | 18 | 11 | 1644 | 1639 | 1646 | |
10374 | 120 | 122 | 124 | 1681 | 1679 | 1677 | 12 | 14 | 16 | 1645 | 1643 | 1641 | |
10374 | 125 | 118 | 123 | 1676 | 1683 | 1678 | 17 | 10 | 15 | 1640 | 1647 | 1642 | |
10374 | 1615 | 1620 | 1613 | 42 | 37 | 44 | 1723 | 1728 | 1721 | 78 | 73 | 80 | |
10374 | 1614 | 1616 | 1618 | 43 | 41 | 39 | 1722 | 1724 | 1726 | 79 | 77 | 75 | |
10374 | 1619 | 1612 | 1617 | 38 | 45 | 40 | 1727 | 1720 | 1725 | 74 | 81 | 76 | |
10374 | 132 | 127 | 134 | 1669 | 1674 | 1667 | 24 | 19 | 26 | 1633 | 1638 | 1631 | |
10374 | 133 | 131 | 129 | 1668 | 1670 | 1672 | 25 | 23 | 21 | 1632 | 1634 | 1636 | |
10374 | 128 | 135 | 130 | 1673 | 1666 | 1671 | 20 | 27 | 22 | 1637 | 1630 | 1635 | |
8 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 1446 | 1441 | 1448 | 211 | 216 | 209 | 1554 | 1549 | 1556 | 247 | 252 | 245 | |
10374 | 1447 | 1445 | 1443 | 210 | 212 | 214 | 1555 | 1553 | 1551 | 246 | 248 | 250 | |
10374 | 1442 | 1449 | 1444 | 215 | 208 | 213 | 1550 | 1557 | 1552 | 251 | 244 | 249 | |
10374 | 265 | 270 | 263 | 1536 | 1531 | 1538 | 157 | 162 | 155 | 1500 | 1495 | 1502 | |
10374 | 264 | 266 | 268 | 1537 | 1535 | 1533 | 156 | 158 | 160 | 1501 | 1499 | 1497 | |
10374 | 269 | 262 | 267 | 1532 | 1539 | 1534 | 161 | 154 | 159 | 1496 | 1503 | 1498 | |
10374 | 1471 | 1476 | 1469 | 186 | 181 | 188 | 1579 | 1584 | 1577 | 222 | 217 | 224 | |
10374 | 1470 | 1472 | 1474 | 187 | 185 | 183 | 1578 | 1580 | 1582 | 223 | 221 | 219 | |
10374 | 1475 | 1468 | 1473 | 182 | 189 | 184 | 1583 | 1576 | 1581 | 218 | 225 | 220 | |
10374 | 276 | 271 | 278 | 1525 | 1530 | 1523 | 168 | 163 | 170 | 1489 | 1494 | 1487 | |
10374 | 277 | 275 | 273 | 1524 | 1526 | 1528 | 169 | 167 | 165 | 1488 | 1490 | 1492 | |
10374 | 272 | 279 | 274 | 1529 | 1522 | 1527 | 164 | 171 | 166 | 1493 | 1486 | 1491 | |
9 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 1302 | 1297 | 1304 | 355 | 360 | 353 | 1410 | 1405 | 1412 | 391 | 396 | 389 | |
10374 | 1303 | 1301 | 1299 | 354 | 356 | 358 | 1411 | 1409 | 1407 | 390 | 392 | 394 | |
10374 | 1298 | 1305 | 1300 | 359 | 352 | 357 | 1406 | 1413 | 1408 | 395 | 388 | 393 | |
10374 | 409 | 414 | 407 | 1392 | 1387 | 1394 | 301 | 306 | 299 | 1356 | 1351 | 1358 | |
10374 | 408 | 410 | 412 | 1393 | 1391 | 1389 | 300 | 302 | 304 | 1357 | 1355 | 1353 | |
10374 | 413 | 406 | 411 | 1388 | 1395 | 1390 | 305 | 298 | 303 | 1352 | 1359 | 1354 | |
10374 | 1327 | 1332 | 1325 | 330 | 325 | 332 | 1435 | 1440 | 1433 | 366 | 361 | 368 | |
10374 | 1326 | 1328 | 1330 | 331 | 329 | 327 | 1434 | 1436 | 1438 | 367 | 365 | 363 | |
10374 | 1331 | 1324 | 1329 | 326 | 333 | 328 | 1439 | 1432 | 1437 | 362 | 369 | 364 | |
10374 | 420 | 415 | 422 | 1381 | 1386 | 1379 | 312 | 307 | 314 | 1345 | 1350 | 1343 | |
10374 | 421 | 419 | 417 | 1380 | 1382 | 1384 | 313 | 311 | 309 | 1344 | 1346 | 1348 | |
10374 | 416 | 423 | 418 | 1385 | 1378 | 1383 | 308 | 315 | 310 | 1349 | 1342 | 1347 | |
10 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 1291 | 1296 | 1289 | 510 | 505 | 512 | 1183 | 1188 | 1181 | 474 | 469 | 476 | |
10374 | 1290 | 1292 | 1294 | 511 | 509 | 507 | 1182 | 1184 | 1186 | 475 | 473 | 471 | |
10374 | 1295 | 1288 | 1293 | 506 | 513 | 508 | 1187 | 1180 | 1185 | 470 | 477 | 472 | |
10374 | 456 | 451 | 458 | 1201 | 1206 | 1199 | 564 | 559 | 566 | 1237 | 1242 | 1235 | |
10374 | 457 | 455 | 453 | 1200 | 1202 | 1204 | 565 | 563 | 561 | 1236 | 1238 | 1240 | |
10374 | 452 | 459 | 454 | 1205 | 1198 | 1203 | 560 | 567 | 562 | 1241 | 1234 | 1239 | |
10374 | 1266 | 1261 | 1268 | 535 | 540 | 533 | 1158 | 1153 | 1160 | 499 | 504 | 497 | |
10374 | 1267 | 1265 | 1263 | 534 | 536 | 538 | 1159 | 1157 | 1155 | 498 | 500 | 502 | |
10374 | 1262 | 1269 | 1264 | 539 | 532 | 537 | 1154 | 1161 | 1156 | 503 | 496 | 501 | |
10374 | 445 | 450 | 443 | 1212 | 1207 | 1214 | 553 | 558 | 551 | 1248 | 1243 | 1250 | |
10374 | 444 | 446 | 448 | 1213 | 1211 | 1209 | 552 | 554 | 556 | 1249 | 1247 | 1245 | |
10374 | 449 | 442 | 447 | 1208 | 1215 | 1210 | 557 | 550 | 555 | 1244 | 1251 | 1246 | |
11 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 1147 | 1152 | 1145 | 654 | 649 | 656 | 1039 | 1044 | 1037 | 618 | 613 | 620 | |
10374 | 1146 | 1148 | 1150 | 655 | 653 | 651 | 1038 | 1040 | 1042 | 619 | 617 | 615 | |
10374 | 1151 | 1144 | 1149 | 650 | 657 | 652 | 1043 | 1036 | 1041 | 614 | 621 | 616 | |
10374 | 600 | 595 | 602 | 1057 | 1062 | 1055 | 708 | 703 | 710 | 1093 | 1098 | 1091 | |
10374 | 601 | 599 | 597 | 1056 | 1058 | 1060 | 709 | 707 | 705 | 1092 | 1094 | 1096 | |
10374 | 596 | 603 | 598 | 1061 | 1054 | 1059 | 704 | 711 | 706 | 1097 | 1090 | 1095 | |
10374 | 1122 | 1117 | 1124 | 679 | 684 | 677 | 1014 | 1009 | 1016 | 643 | 648 | 641 | |
10374 | 1123 | 1121 | 1119 | 678 | 680 | 682 | 1015 | 1013 | 1011 | 642 | 644 | 646 | |
10374 | 1118 | 1125 | 1120 | 683 | 676 | 681 | 1010 | 1017 | 1012 | 647 | 640 | 645 | |
10374 | 589 | 594 | 587 | 1068 | 1063 | 1070 | 697 | 702 | 695 | 1104 | 1099 | 1106 | |
10374 | 588 | 590 | 592 | 1069 | 1067 | 1065 | 696 | 698 | 700 | 1105 | 1103 | 1101 | |
10374 | 593 | 586 | 591 | 1064 | 1071 | 1066 | 701 | 694 | 699 | 1100 | 1107 | 1102 | |
12 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | 10374 | |
10374 | 1003 | 1008 | 1001 | 798 | 793 | 800 | 895 | 900 | 893 | 762 | 757 | 764 | |
10374 | 1002 | 1004 | 1006 | 799 | 797 | 795 | 894 | 896 | 898 | 763 | 761 | 759 | |
10374 | 1007 | 1000 | 1005 | 794 | 801 | 796 | 899 | 892 | 897 | 758 | 765 | 760 | |
10374 | 744 | 739 | 746 | 913 | 918 | 911 | 852 | 847 | 854 | 949 | 954 | 947 | |
10374 | 745 | 743 | 741 | 912 | 914 | 916 | 853 | 851 | 849 | 948 | 950 | 952 | |
10374 | 740 | 747 | 742 | 917 | 910 | 915 | 848 | 855 | 850 | 953 | 946 | 951 | |
10374 | 978 | 973 | 980 | 823 | 828 | 821 | 870 | 865 | 872 | 787 | 792 | 785 | |
10374 | 979 | 977 | 975 | 822 | 824 | 826 | 871 | 869 | 867 | 786 | 788 | 790 | |
10374 | 974 | 981 | 976 | 827 | 820 | 825 | 866 | 873 | 868 | 791 | 784 | 789 | |
10374 | 733 | 738 | 731 | 924 | 919 | 926 | 841 | 846 | 839 | 960 | 955 | 962 | |
10374 | 732 | 734 | 736 | 925 | 923 | 921 | 840 | 842 | 844 | 961 | 959 | 957 | |
10374 | 737 | 730 | 735 | 920 | 927 | 922 | 845 | 838 | 843 | 956 | 963 | 958 |
N.B.: In the download below I have adjusted the second grid, so in all levels of the 12x12x12 pantriagonal cube the main diagonals give the magic sum.
With method composite 1 you use a magic square to construct a magic cube. See on this website the construction of:
3x3x3 (simple), 4x4x4 (most perfect), 5x5x5 (pantriagonal), 7x7x7 (pantriagonal),
9x9x9 (pandiagonal & compact), 12x12x12 (diagonal), 12x12x12 (pantriagonal),
15x15x15 (pandiagonal & compact), 16x16x16 (Nasik)a, 16x16x16 (Nasik)b,
20x20x20 (diagonal), 20x20x20 (pantriagonal), 24x24x24 (diagonal), 24x24x24
(pantriagonal), 28x28x28 (diagonal), 28x28x28 (pantriagonal)