30x30x30 magic cube

Diagonal 30x30x30 magic cube (Composite 4)

 

Using a diagonal 5x5x5 magic cube and a diagonal 6x6x6 magic cube, there are three possibilities to construct a diagonal 30x30x30 magic cube.

 

Take as first grid 125x diagonal 6x6x6 magic cube and as second grid 216x diagonal 5x5x5 magic cube. See below the grids and the result of level 1.

 

 

Take 1x number from first grid with 125x diagonal 6x6x6 magic cube [level 1]

109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107
109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112 109 143 76 123 88 112
87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126 87 156 49 170 63 126
140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82 140 174 52 150 53 82
75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138 75 66 182 51 139 138
136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86 136 40 148 65 176 86
104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107 104 72 144 92 132 107

 

 

+216x (number -/- 1) from second grid with 216x diagonal 5x5x5 magic cube [level 1]

67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5
116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95
40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79
56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35
36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101
67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5
116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95
40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79
56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35
36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101
67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5
116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95
40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79
56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35
36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101
67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5
116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95
40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79
56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35
36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101
67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5
116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95
40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79
56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35
36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101
67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5 67 18 119 106 5
116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95 116 17 14 73 95
40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79 40 50 81 65 79
56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35 56 120 55 49 35
36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101 36 110 46 22 101

 

 

= 30x30x30 diagonal magic cube [level 1]

14365 3815 25564 22803 952 14368 3781 25631 22756 987 14344 3784 25597 22823 940 14379 3760 25600 22789 1007 14332 3795 25576 22792 973 14399 3748 25611 22768 976
24927 3612 2857 15722 20367 24966 3543 2964 15601 20474 24903 3582 2895 15708 20353 25010 3519 2934 15639 20460 24889 3626 2871 15678 20391 24996 3505 2978 15615 20430
8564 10758 17332 13974 16901 8506 10724 17454 13876 16998 8477 10666 17420 13998 16900 8574 10637 17362 13964 17022 8476 10734 17333 13906 16988 8598 10636 17430 13877 16930
11955 25770 11846 10419 7483 12018 25779 11730 10550 7395 12019 25842 11739 10434 7526 11931 25843 11802 10443 7410 12062 25755 11803 10506 7419 11946 25886 11715 10507 7482
7696 23584 9868 4601 21776 7646 23680 9760 4684 21665 7736 23630 9856 4576 21748 7625 23720 9806 4672 21640 7708 23609 9896 4622 21736 7600 23692 9785 4712 21686
14360 3744 25632 22772 996 14363 3776 25560 22824 956 14388 3779 25592 22752 1008 14348 3804 25595 22784 936 14400 3764 25620 22787 968 14328 3816 25580 22812 971
24949 3599 2884 15675 20392 24952 3565 2951 15628 20427 24928 3568 2917 15695 20380 24963 3544 2920 15661 20447 24916 3579 2896 15664 20413 24983 3532 2931 15640 20416
8511 10740 17329 13994 16911 8550 10671 17436 13873 17018 8487 10710 17367 13980 16897 8594 10647 17406 13911 17004 8473 10754 17343 13950 16935 8580 10633 17450 13887 16974
12020 25878 11716 10518 7397 11962 25844 11838 10420 7494 11933 25786 11804 10542 7396 12030 25757 11746 10508 7518 11932 25854 11717 10450 7484 12054 25756 11814 10421 7426
7635 23610 9902 4587 21739 7698 23619 9786 4718 21651 7699 23682 9795 4602 21782 7611 23683 9858 4611 21666 7742 23595 9859 4674 21675 7626 23726 9771 4675 21738
14392 3712 25636 22745 1040 14342 3808 25528 22828 929 14432 3758 25624 22720 1012 14321 3848 25574 22816 904 14404 3737 25664 22766 1000 14296 3820 25553 22856 950
24944 3528 2952 15644 20436 24947 3560 2880 15696 20396 24972 3563 2912 15624 20448 24932 3588 2915 15656 20376 24984 3548 2940 15659 20408 24912 3600 2900 15684 20411
8533 10727 17356 13947 16936 8536 10693 17423 13900 16971 8512 10696 17389 13967 16924 8547 10672 17392 13933 16991 8500 10707 17368 13936 16957 8567 10660 17403 13912 16960
11967 25860 11713 10538 7407 12006 25791 11820 10417 7514 11943 25830 11751 10524 7393 12050 25767 11790 10455 7500 11929 25874 11727 10494 7431 12036 25753 11834 10431 7470
7700 23718 9772 4686 21653 7642 23684 9894 4588 21750 7613 23626 9860 4710 21652 7710 23597 9802 4676 21774 7612 23694 9773 4618 21740 7734 23596 9870 4589 21682
14331 3738 25670 22731 1003 14394 3747 25554 22862 915 14395 3810 25563 22746 1046 14307 3811 25626 22755 930 14438 3723 25627 22818 939 14322 3854 25539 22819 1002
24976 3496 2956 15617 20480 24926 3592 2848 15700 20369 25016 3542 2944 15592 20452 24905 3632 2894 15688 20344 24988 3521 2984 15638 20440 24880 3604 2873 15728 20390
8528 10656 17424 13916 16980 8531 10688 17352 13968 16940 8556 10691 17384 13896 16992 8516 10716 17387 13928 16920 8568 10676 17412 13931 16952 8496 10728 17372 13956 16955
11989 25847 11740 10491 7432 11992 25813 11807 10444 7467 11968 25816 11773 10511 7420 12003 25792 11776 10477 7487 11956 25827 11752 10480 7453 12023 25780 11787 10456 7456
7647 23700 9769 4706 21663 7686 23631 9876 4585 21770 7623 23670 9807 4692 21649 7730 23607 9846 4623 21756 7609 23714 9783 4662 21687 7716 23593 9890 4599 21726
14396 3846 25540 22830 917 14338 3812 25662 22732 1014 14309 3754 25628 22854 916 14406 3725 25570 22820 1038 14308 3822 25541 22762 1004 14430 3724 25638 22733 946
24915 3522 2990 15603 20443 24978 3531 2874 15734 20355 24979 3594 2883 15618 20486 24891 3595 2946 15627 20370 25022 3507 2947 15690 20379 24906 3638 2859 15691 20442
8560 10624 17428 13889 17024 8510 10720 17320 13972 16913 8600 10670 17416 13864 16996 8489 10760 17366 13960 16888 8572 10649 17456 13910 16984 8464 10732 17345 14000 16934
11984 25776 11808 10460 7476 11987 25808 11736 10512 7436 12012 25811 11768 10440 7488 11972 25836 11771 10472 7416 12024 25796 11796 10475 7448 11952 25848 11756 10500 7451
7669 23687 9796 4659 21688 7672 23653 9863 4612 21723 7648 23656 9829 4679 21676 7683 23632 9832 4645 21743 7636 23667 9808 4648 21709 7703 23620 9843 4624 21712
14343 3828 25537 22850 927 14382 3759 25644 22729 1034 14319 3798 25575 22836 913 14426 3735 25614 22767 1020 14305 3842 25551 22806 951 14412 3721 25658 22743 990
24980 3630 2860 15702 20357 24922 3596 2982 15604 20454 24893 3538 2948 15726 20356 24990 3509 2890 15692 20478 24892 3606 2861 15634 20444 25014 3508 2958 15605 20386
8499 10650 17462 13875 16987 8562 10659 17346 14006 16899 8563 10722 17355 13890 17030 8475 10723 17418 13899 16914 8606 10635 17419 13962 16923 8490 10766 17331 13963 16986
12016 25744 11812 10433 7520 11966 25840 11704 10516 7409 12056 25790 11800 10408 7492 11945 25880 11750 10504 7384 12028 25769 11840 10454 7480 11920 25852 11729 10544 7430
7664 23616 9864 4628 21732 7667 23648 9792 4680 21692 7692 23651 9824 4608 21744 7652 23676 9827 4640 21672 7704 23636 9852 4643 21704 7632 23688 9812 4668 21707

 

 

N.B.: Extra magic feature is that each random chosen 5x6 or 6x5 rectangle in the levels and horizontal/vertical through the levels (= 5x6 and 6x5 compact in all three directions) give the magic sum.

 

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 composite 4 you use AxAxAx magic cube of order B and BxBxBx magic cube of order A or vice versa to construct a magic cube of order AxB. See on this website the construction of:

12x12x12 (simple), 20x20x20 (pantriagonal), 28x28x28 (pantriagonal),

30x30x30 (diagonal) and 30x30x30 (pantriagonal)

 

Download
30x30x30, diagonal (3).xlsx
Microsoft Excel werkblad 1.9 MB
Download
30x30x30 magic cube