### 30x30x30 pantriagonal magic cube (5)

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Use the method of the 24x24x24 magic cube to construct a 30x30x30 magic cube.

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Construct the 30x30x30 pantriagonal cube by using three grids.

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The first grid consists of 125x pantriagonal 6x6x6 magic cube.

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The second grid consists of the 5x5 panmagic square. See below the first level.

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Second grid ofÂ pantriagonal 30x30x30 magic cube, level 1

 1 25 1 25 1 25 15 11 15 11 15 11 22 4 22 4 22 4 18 8 18 8 18 8 9 17 9 17 9 17 25 1 25 1 25 1 11 15 11 15 11 15 4 22 4 22 4 22 8 18 8 18 8 18 17 9 17 9 17 9 1 25 1 25 1 25 15 11 15 11 15 11 22 4 22 4 22 4 18 8 18 8 18 8 9 17 9 17 9 17 25 1 25 1 25 1 11 15 11 15 11 15 4 22 4 22 4 22 8 18 8 18 8 18 17 9 17 9 17 9 1 25 1 25 1 25 15 11 15 11 15 11 22 4 22 4 22 4 18 8 18 8 18 8 9 17 9 17 9 17 25 1 25 1 25 1 11 15 11 15 11 15 4 22 4 22 4 22 8 18 8 18 8 18 17 9 17 9 17 9 23 3 23 3 23 3 19 7 19 7 19 7 6 20 6 20 6 20 5 21 5 21 5 21 12 14 12 14 12 14 3 23 3 23 3 23 7 19 7 19 7 19 20 6 20 6 20 6 21 5 21 5 21 5 14 12 14 12 14 12 23 3 23 3 23 3 19 7 19 7 19 7 6 20 6 20 6 20 5 21 5 21 5 21 12 14 12 14 12 14 3 23 3 23 3 23 7 19 7 19 7 19 20 6 20 6 20 6 21 5 21 5 21 5 14 12 14 12 14 12 23 3 23 3 23 3 19 7 19 7 19 7 6 20 6 20 6 20 5 21 5 21 5 21 12 14 12 14 12 14 3 23 3 23 3 23 7 19 7 19 7 19 20 6 20 6 20 6 21 5 21 5 21 5 14 12 14 12 14 12 10 16 10 16 10 16 2 24 2 24 2 24 13 13 13 13 13 13 24 2 24 2 24 2 16 10 16 10 16 10 16 10 16 10 16 10 24 2 24 2 24 2 13 13 13 13 13 13 2 24 2 24 2 24 10 16 10 16 10 16 10 16 10 16 10 16 2 24 2 24 2 24 13 13 13 13 13 13 24 2 24 2 24 2 16 10 16 10 16 10 16 10 16 10 16 10 24 2 24 2 24 2 13 13 13 13 13 13 2 24 2 24 2 24 10 16 10 16 10 16 10 16 10 16 10 16 2 24 2 24 2 24 13 13 13 13 13 13 24 2 24 2 24 2 16 10 16 10 16 10 16 10 16 10 16 10 24 2 24 2 24 2 13 13 13 13 13 13 2 24 2 24 2 24 10 16 10 16 10 16 14 12 14 12 14 12 21 5 21 5 21 5 20 6 20 6 20 6 7 19 7 19 7 19 3 23 3 23 3 23 12 14 12 14 12 14 5 21 5 21 5 21 6 20 6 20 6 20 19 7 19 7 19 7 23 3 23 3 23 3 14 12 14 12 14 12 21 5 21 5 21 5 20 6 20 6 20 6 7 19 7 19 7 19 3 23 3 23 3 23 12 14 12 14 12 14 5 21 5 21 5 21 6 20 6 20 6 20 19 7 19 7 19 7 23 3 23 3 23 3 14 12 14 12 14 12 21 5 21 5 21 5 20 6 20 6 20 6 7 19 7 19 7 19 3 23 3 23 3 23 12 14 12 14 12 14 5 21 5 21 5 21 6 20 6 20 6 20 19 7 19 7 19 7 23 3 23 3 23 3 17 9 17 9 17 9 8 18 8 18 8 18 4 22 4 22 4 22 11 15 11 15 11 15 25 1 25 1 25 1 9 17 9 17 9 17 18 8 18 8 18 8 22 4 22 4 22 4 15 11 15 11 15 11 1 25 1 25 1 25 17 9 17 9 17 9 8 18 8 18 8 18 4 22 4 22 4 22 11 15 11 15 11 15 25 1 25 1 25 1 9 17 9 17 9 17 18 8 18 8 18 8 22 4 22 4 22 4 15 11 15 11 15 11 1 25 1 25 1 25 17 9 17 9 17 9 8 18 8 18 8 18 4 22 4 22 4 22 11 15 11 15 11 15 25 1 25 1 25 1 9 17 9 17 9 17 18 8 18 8 18 8 22 4 22 4 22 4 15 11 15 11 15 11 1 25 1 25 1 25

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The second and third level are exactly the same as the first level and level 4 up to 6 consist of the inverse numbers. Level 7 up to 30 repeats level 1 up to 6.

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The third grid consists of the numbers 0 up to 4. ee below the first level.

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Third grid ofÂ pantriagonal 30x30x30 magic cube, level 1

 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0

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The second and third level are exactly the same as the first level and level 4 up to 6 consist of the inverse numbers. Level 7 up to 30 repeats level 1 up to 6.

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Take 1x number from first grid + 216x (number -/- 1) from second grid + 216x25x number from third grid and you get the following result.

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30x30x30 pantriagonal magic cube,Â consisting ofÂ 125x pantriagonal 4x4x4, level 1

 1 26880 116 26982 175 26849 3025 23856 3140 23958 3199 23825 4537 22344 4652 22446 4711 22313 3673 23208 3788 23310 3847 23177 1729 25152 1844 25254 1903 25121 26879 115 26787 176 26850 196 23855 3139 23763 3200 23826 3220 22343 4651 22251 4712 22314 4732 23207 3787 23115 3848 23178 3868 25151 1843 25059 1904 25122 1924 117 26786 94 26848 197 26961 3141 23762 3118 23824 3221 23937 4653 22250 4630 22312 4733 22425 3789 23114 3766 23176 3869 23289 1845 25058 1822 25120 1925 25233 26973 166 26867 10 26844 143 23949 3190 23843 3034 23820 3167 22437 4702 22331 4546 22308 4679 23301 3838 23195 3682 23172 3815 25245 1894 25139 1738 25116 1871 167 26868 187 26843 142 26796 3191 23844 3211 23819 3166 23772 4703 22332 4723 22307 4678 22260 3839 23196 3859 23171 3814 23124 1895 25140 1915 25115 1870 25068 26866 188 26952 144 26795 58 23842 3212 23928 3168 23771 3082 22330 4724 22416 4680 22259 4594 23194 3860 23280 3816 23123 3730 25138 1916 25224 1872 25067 1786 4753 22128 4868 22230 4927 22097 3889 22992 4004 23094 4063 22961 1081 25800 1196 25902 1255 25769 865 26016 980 26118 1039 25985 2377 24504 2492 24606 2551 24473 22127 4867 22035 4928 22098 4948 22991 4003 22899 4064 22962 4084 25799 1195 25707 1256 25770 1276 26015 979 25923 1040 25986 1060 24503 2491 24411 2552 24474 2572 4869 22034 4846 22096 4949 22209 4005 22898 3982 22960 4085 23073 1197 25706 1174 25768 1277 25881 981 25922 958 25984 1061 26097 2493 24410 2470 24472 2573 24585 22221 4918 22115 4762 22092 4895 23085 4054 22979 3898 22956 4031 25893 1246 25787 1090 25764 1223 26109 1030 26003 874 25980 1007 24597 2542 24491 2386 24468 2519 4919 22116 4939 22091 4894 22044 4055 22980 4075 22955 4030 22908 1247 25788 1267 25763 1222 25716 1031 26004 1051 25979 1006 25932 2543 24492 2563 24467 2518 24420 22114 4940 22200 4896 22043 4810 22978 4076 23064 4032 22907 3946 25786 1268 25872 1224 25715 1138 26002 1052 26088 1008 25931 922 24490 2564 24576 2520 24419 2434 1945 24936 2060 25038 2119 24905 217 26664 332 26766 391 26633 2593 24288 2708 24390 2767 24257 4969 21912 5084 22014 5143 21881 3241 23640 3356 23742 3415 23609 24935 2059 24843 2120 24906 2140 26663 331 26571 392 26634 412 24287 2707 24195 2768 24258 2788 21911 5083 21819 5144 21882 5164 23639 3355 23547 3416 23610 3436 2061 24842 2038 24904 2141 25017 333 26570 310 26632 413 26745 2709 24194 2686 24256 2789 24369 5085 21818 5062 21880 5165 21993 3357 23546 3334 23608 3437 23721 25029 2110 24923 1954 24900 2087 26757 382 26651 226 26628 359 24381 2758 24275 2602 24252 2735 22005 5134 21899 4978 21876 5111 23733 3406 23627 3250 23604 3383 2111 24924 2131 24899 2086 24852 383 26652 403 26627 358 26580 2759 24276 2779 24251 2734 24204 5135 21900 5155 21875 5110 21828 3407 23628 3427 23603 3382 23556 24922 2132 25008 2088 24851 2002 26650 404 26736 360 26579 274 24274 2780 24360 2736 24203 2650 21898 5156 21984 5112 21827 5026 23626 3428 23712 3384 23555 3298 2809 24072 2924 24174 2983 24041 4321 22560 4436 22662 4495 22529 4105 22776 4220 22878 4279 22745 1297 25584 1412 25686 1471 25553 433 26448 548 26550 607 26417 24071 2923 23979 2984 24042 3004 22559 4435 22467 4496 22530 4516 22775 4219 22683 4280 22746 4300 25583 1411 25491 1472 25554 1492 26447 547 26355 608 26418 628 2925 23978 2902 24040 3005 24153 4437 22466 4414 22528 4517 22641 4221 22682 4198 22744 4301 22857 1413 25490 1390 25552 1493 25665 549 26354 526 26416 629 26529 24165 2974 24059 2818 24036 2951 22653 4486 22547 4330 22524 4463 22869 4270 22763 4114 22740 4247 25677 1462 25571 1306 25548 1439 26541 598 26435 442 26412 575 2975 24060 2995 24035 2950 23988 4487 22548 4507 22523 4462 22476 4271