Pantriagonal 24x24x24 magic cube (Medjig method 3D)
See for explantion about the Medjig method to construct a magic square: 6x6 magic square.
Use two grids to construct a 24x24x24 diagonal magic cube. The first grid consists of a 2x2x2 'blown up' pantriagonal 12x12x12 magic cube. The second grid does not consist of the 2x2 Medjig tiles with the numbers 0 up to 3, but consists of the 2x2x2 Medjig blocks with the numbers 0 up to 7. See below the grids and result of level 1.
Take 1x number from 1st grid with 2x2x2 'blown up' pantriagonal 12x12x12 [level 1]
| 8 | 8 | 15 | 15 | 19 | 19 | 1493 | 1493 | 1500 | 1500 | 1504 | 1504 | 332 | 332 | 339 | 339 | 343 | 343 | 1601 | 1601 | 1608 | 1608 | 1612 | 1612 |
| 8 | 8 | 15 | 15 | 19 | 19 | 1493 | 1493 | 1500 | 1500 | 1504 | 1504 | 332 | 332 | 339 | 339 | 343 | 343 | 1601 | 1601 | 1608 | 1608 | 1612 | 1612 |
| 12 | 12 | 25 | 25 | 5 | 5 | 1497 | 1497 | 1510 | 1510 | 1490 | 1490 | 336 | 336 | 349 | 349 | 329 | 329 | 1605 | 1605 | 1618 | 1618 | 1598 | 1598 |
| 12 | 12 | 25 | 25 | 5 | 5 | 1497 | 1497 | 1510 | 1510 | 1490 | 1490 | 336 | 336 | 349 | 349 | 329 | 329 | 1605 | 1605 | 1618 | 1618 | 1598 | 1598 |
| 22 | 22 | 2 | 2 | 18 | 18 | 1507 | 1507 | 1487 | 1487 | 1503 | 1503 | 346 | 346 | 326 | 326 | 342 | 342 | 1615 | 1615 | 1595 | 1595 | 1611 | 1611 |
| 22 | 22 | 2 | 2 | 18 | 18 | 1507 | 1507 | 1487 | 1487 | 1503 | 1503 | 346 | 346 | 326 | 326 | 342 | 342 | 1615 | 1615 | 1595 | 1595 | 1611 | 1611 |
| 1682 | 1682 | 1689 | 1689 | 1693 | 1693 | 251 | 251 | 258 | 258 | 262 | 262 | 1358 | 1358 | 1365 | 1365 | 1369 | 1369 | 143 | 143 | 150 | 150 | 154 | 154 |
| 1682 | 1682 | 1689 | 1689 | 1693 | 1693 | 251 | 251 | 258 | 258 | 262 | 262 | 1358 | 1358 | 1365 | 1365 | 1369 | 1369 | 143 | 143 | 150 | 150 | 154 | 154 |
| 1686 | 1686 | 1699 | 1699 | 1679 | 1679 | 255 | 255 | 268 | 268 | 248 | 248 | 1362 | 1362 | 1375 | 1375 | 1355 | 1355 | 147 | 147 | 160 | 160 | 140 | 140 |
| 1686 | 1686 | 1699 | 1699 | 1679 | 1679 | 255 | 255 | 268 | 268 | 248 | 248 | 1362 | 1362 | 1375 | 1375 | 1355 | 1355 | 147 | 147 | 160 | 160 | 140 | 140 |
| 1696 | 1696 | 1676 | 1676 | 1692 | 1692 | 265 | 265 | 245 | 245 | 261 | 261 | 1372 | 1372 | 1352 | 1352 | 1368 | 1368 | 157 | 157 | 137 | 137 | 153 | 153 |
| 1696 | 1696 | 1676 | 1676 | 1692 | 1692 | 265 | 265 | 245 | 245 | 261 | 261 | 1372 | 1372 | 1352 | 1352 | 1368 | 1368 | 157 | 157 | 137 | 137 | 153 | 153 |
| 89 | 89 | 96 | 96 | 100 | 100 | 1412 | 1412 | 1419 | 1419 | 1423 | 1423 | 413 | 413 | 420 | 420 | 424 | 424 | 1520 | 1520 | 1527 | 1527 | 1531 | 1531 |
| 89 | 89 | 96 | 96 | 100 | 100 | 1412 | 1412 | 1419 | 1419 | 1423 | 1423 | 413 | 413 | 420 | 420 | 424 | 424 | 1520 | 1520 | 1527 | 1527 | 1531 | 1531 |
| 93 | 93 | 106 | 106 | 86 | 86 | 1416 | 1416 | 1429 | 1429 | 1409 | 1409 | 417 | 417 | 430 | 430 | 410 | 410 | 1524 | 1524 | 1537 | 1537 | 1517 | 1517 |
| 93 | 93 | 106 | 106 | 86 | 86 | 1416 | 1416 | 1429 | 1429 | 1409 | 1409 | 417 | 417 | 430 | 430 | 410 | 410 | 1524 | 1524 | 1537 | 1537 | 1517 | 1517 |
| 103 | 103 | 83 | 83 | 99 | 99 | 1426 | 1426 | 1406 | 1406 | 1422 | 1422 | 427 | 427 | 407 | 407 | 423 | 423 | 1534 | 1534 | 1514 | 1514 | 1530 | 1530 |
| 103 | 103 | 83 | 83 | 99 | 99 | 1426 | 1426 | 1406 | 1406 | 1422 | 1422 | 427 | 427 | 407 | 407 | 423 | 423 | 1534 | 1534 | 1514 | 1514 | 1530 | 1530 |
| 1655 | 1655 | 1662 | 1662 | 1666 | 1666 | 278 | 278 | 285 | 285 | 289 | 289 | 1331 | 1331 | 1338 | 1338 | 1342 | 1342 | 170 | 170 | 177 | 177 | 181 | 181 |
| 1655 | 1655 | 1662 | 1662 | 1666 | 1666 | 278 | 278 | 285 | 285 | 289 | 289 | 1331 | 1331 | 1338 | 1338 | 1342 | 1342 | 170 | 170 | 177 | 177 | 181 | 181 |
| 1659 | 1659 | 1672 | 1672 | 1652 | 1652 | 282 | 282 | 295 | 295 | 275 | 275 | 1335 | 1335 | 1348 | 1348 | 1328 | 1328 | 174 | 174 | 187 | 187 | 167 | 167 |
| 1659 | 1659 | 1672 | 1672 | 1652 | 1652 | 282 | 282 | 295 | 295 | 275 | 275 | 1335 | 1335 | 1348 | 1348 | 1328 | 1328 | 174 | 174 | 187 | 187 | 167 | 167 |
| 1669 | 1669 | 1649 | 1649 | 1665 | 1665 | 292 | 292 | 272 | 272 | 288 | 288 | 1345 | 1345 | 1325 | 1325 | 1341 | 1341 | 184 | 184 | 164 | 164 | 180 | 180 |
| 1669 | 1669 | 1649 | 1649 | 1665 | 1665 | 292 | 292 | 272 | 272 | 288 | 288 | 1345 | 1345 | 1325 | 1325 | 1341 | 1341 | 184 | 184 | 164 | 164 | 180 | 180 |
+ 1.728x number from 2nd grid with 2x2x2 Medjig blocks [level 1]
| 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 |
| 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 |
| 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 |
| 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 |
| 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 |
| 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 |
| 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 |
| 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 |
| 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 |
| 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 |
| 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 |
| 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 |
| 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 |
| 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 |
| 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 |
| 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 |
| 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 |
| 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 |
| 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 |
| 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 |
| 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 |
| 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 |
| 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 | 4 | 2 | 7 | 1 | 3 | 5 | 0 | 6 |
| 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 | 7 | 1 | 4 | 2 | 0 | 6 | 3 | 5 |
= 24x24x24 pantriagonal magic cube [level 1]
| 8 | 10376 | 5199 | 8655 | 12115 | 1747 | 8405 | 4949 | 1500 | 11868 | 6688 | 10144 | 12428 | 2060 | 7251 | 3795 | 343 | 10711 | 6785 | 10241 | 13704 | 3336 | 8524 | 5068 |
| 5192 | 8648 | 15 | 10383 | 6931 | 3475 | 13589 | 3221 | 6684 | 10140 | 1504 | 11872 | 7244 | 3788 | 12435 | 2067 | 5527 | 8983 | 1601 | 11969 | 8520 | 5064 | 13708 | 3340 |
| 6924 | 3468 | 12121 | 1753 | 5189 | 8645 | 1497 | 11865 | 8422 | 4966 | 13586 | 3218 | 5520 | 8976 | 349 | 10717 | 7241 | 3785 | 13701 | 3333 | 6802 | 10258 | 1598 | 11966 |
| 12108 | 1740 | 6937 | 3481 | 5 | 10373 | 6681 | 10137 | 13606 | 3238 | 8402 | 4946 | 336 | 10704 | 5533 | 8989 | 12425 | 2057 | 8517 | 5061 | 1618 | 11986 | 6782 | 10238 |
| 22 | 10390 | 5186 | 8642 | 12114 | 1746 | 8419 | 4963 | 1487 | 11855 | 6687 | 10143 | 12442 | 2074 | 7238 | 3782 | 342 | 10710 | 6799 | 10255 | 13691 | 3323 | 8523 | 5067 |
| 5206 | 8662 | 2 | 10370 | 6930 | 3474 | 13603 | 3235 | 6671 | 10127 | 1503 | 11871 | 7258 | 3802 | 12422 | 2054 | 5526 | 8982 | 1615 | 11983 | 8507 | 5051 | 13707 | 3339 |
| 8594 | 5138 | 13785 | 3417 | 6877 | 10333 | 251 | 10619 | 7170 | 3714 | 12358 | 1990 | 6542 | 9998 | 1365 | 11733 | 8281 | 4825 | 12239 | 1871 | 5334 | 8790 | 154 | 10522 |
| 13778 | 3410 | 8601 | 5145 | 1693 | 12061 | 5435 | 8891 | 12354 | 1986 | 7174 | 3718 | 1358 | 11726 | 6549 | 10005 | 13465 | 3097 | 7055 | 3599 | 150 | 10518 | 5338 | 8794 |
| 1686 | 12054 | 6883 | 10339 | 13775 | 3407 | 7167 | 3711 | 268 | 10636 | 5432 | 8888 | 13458 | 3090 | 8287 | 4831 | 1355 | 11723 | 5331 | 8787 | 12256 | 1888 | 7052 | 3596 |
| 6870 | 10326 | 1699 | 12067 | 8591 | 5135 | 12351 | 1983 | 5452 | 8908 | 248 | 10616 | 8274 | 4818 | 13471 | 3103 | 6539 | 9995 | 147 | 10515 | 7072 | 3616 | 12236 | 1868 |
| 8608 | 5152 | 13772 | 3404 | 6876 | 10332 | 265 | 10633 | 7157 | 3701 | 12357 | 1989 | 6556 | 10012 | 1352 | 11720 | 8280 | 4824 | 12253 | 1885 | 5321 | 8777 | 153 | 10521 |
| 13792 | 3424 | 8588 | 5132 | 1692 | 12060 | 5449 | 8905 | 12341 | 1973 | 7173 | 3717 | 1372 | 11740 | 6536 | 9992 | 13464 | 3096 | 7069 | 3613 | 137 | 10505 | 5337 | 8793 |
| 89 | 10457 | 5280 | 8736 | 12196 | 1828 | 8324 | 4868 | 1419 | 11787 | 6607 | 10063 | 12509 | 2141 | 7332 | 3876 | 424 | 10792 | 6704 | 10160 | 13623 | 3255 | 8443 | 4987 |
| 5273 | 8729 | 96 | 10464 | 7012 | 3556 | 13508 | 3140 | 6603 | 10059 | 1423 | 11791 | 7325 | 3869 | 12516 | 2148 | 5608 | 9064 | 1520 | 11888 | 8439 | 4983 | 13627 | 3259 |
| 7005 | 3549 | 12202 | 1834 | 5270 | 8726 | 1416 | 11784 | 8341 | 4885 | 13505 | 3137 | 5601 | 9057 | 430 | 10798 | 7322 | 3866 | 13620 | 3252 | 6721 | 10177 | 1517 | 11885 |
| 12189 | 1821 | 7018 | 3562 | 86 | 10454 | 6600 | 10056 | 13525 | 3157 | 8321 | 4865 | 417 | 10785 | 5614 | 9070 | 12506 | 2138 | 8436 | 4980 | 1537 | 11905 | 6701 | 10157 |
| 103 | 10471 | 5267 | 8723 | 12195 | 1827 | 8338 | 4882 | 1406 | 11774 | 6606 | 10062 | 12523 | 2155 | 7319 | 3863 | 423 | 10791 | 6718 | 10174 | 13610 | 3242 | 8442 | 4986 |
| 5287 | 8743 | 83 | 10451 | 7011 | 3555 | 13522 | 3154 | 6590 | 10046 | 1422 | 11790 | 7339 | 3883 | 12503 | 2135 | 5607 | 9063 | 1534 | 11902 | 8426 | 4970 | 13626 | 3258 |
| 8567 | 5111 | 13758 | 3390 | 6850 | 10306 | 278 | 10646 | 7197 | 3741 | 12385 | 2017 | 6515 | 9971 | 1338 | 11706 | 8254 | 4798 | 12266 | 1898 | 5361 | 8817 | 181 | 10549 |
| 13751 | 3383 | 8574 | 5118 | 1666 | 12034 | 5462 | 8918 | 12381 | 2013 | 7201 | 3745 | 1331 | 11699 | 6522 | 9978 | 13438 | 3070 | 7082 | 3626 | 177 | 10545 | 5365 | 8821 |
| 1659 | 12027 | 6856 | 10312 | 13748 | 3380 | 7194 | 3738 | 295 | 10663 | 5459 | 8915 | 13431 | 3063 | 8260 | 4804 | 1328 | 11696 | 5358 | 8814 | 12283 | 1915 | 7079 | 3623 |
| 6843 | 10299 | 1672 | 12040 | 8564 | 5108 | 12378 | 2010 | 5479 | 8935 | 275 | 10643 | 8247 | 4791 | 13444 | 3076 | 6512 | 9968 | 174 | 10542 | 7099 | 3643 | 12263 | 1895 |
| 8581 | 5125 | 13745 | 3377 | 6849 | 10305 | 292 | 10660 | 7184 | 3728 | 12384 | 2016 | 6529 | 9985 | 1325 | 11693 | 8253 | 4797 | 12280 | 1912 | 5348 | 8804 | 180 | 10548 |
| 13765 | 3397 | 8561 | 5105 | 1665 | 12033 | 5476 | 8932 | 12368 | 2000 | 7200 | 3744 | 1345 | 11713 | 6509 | 9965 | 13437 | 3069 | 7096 | 3640 | 164 | 10532 | 5364 | 8820 |
See for all levels and check if all numbers are in the magic cube and addition of the numbers give the right magic sum, the download below.
With method of Medjig you can construct a magic cube of even order. See on this website the construction of:
6x6x6 (simple), 8x8x8 (pantriagonal), 10x10x10 (simple), 10x10x10 (pantriagonal), 12x12x12 (pantriagonal), 14x14x14 (pantriagonal), 16x16x16 (Nasik), 20x20x20 (pantriagonal), 22x22x22 (pantriagonal), 24x24x24 (diagonal), 24x24x24 (pantriagonal), 26x26x26 (pantriagonal), 28x28x28 (pantriagonal) and 32x32x32 (Nasik)
