### 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:

24x24x24, Pantriagonal (Medjig).xlsx