Pantriagonal 28x28x28 magic cube consisting of 343x proportional pantriagonal 4x4x4 magic cube (composite 5)

 

Use a pantriagonal 4x4x4 magic cube and a panmagic 7x7 square to construct a pantriagonal 28x28x28 magic cube, consisting of 343 proportional pantriagonal 4x4x4 magic cubes.

 

The first griod consists of 343x pantriagonal 4x4x4 magic cube. The second grids consists of the 7x7 panmagic square and its inverse. The third grid consists of the numbers 0 up to 6. Take 1x number from first grid + 64 x (number -/- 1) from second grid + 64x49x number from third grid. See the grids and the results of the first level below.

 

 

Take 1x number from first grid of 28x28x28 magic cube [level 1] 

6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24
6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24
6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24
6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24
6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24
6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24
6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43
51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30
16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33
57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24

 

 

 

+ 64x (number -/- 1) from second grid of 28x28x28 magic cube [level 1]

1 49 1 49 35 15 35 15 16 34 16 34 45 5 45 5 39 11 39 11 26 24 26 24 13 37 13 37
49 1 49 1 15 35 15 35 34 16 34 16 5 45 5 45 11 39 11 39 24 26 24 26 37 13 37 13
1 49 1 49 35 15 35 15 16 34 16 34 45 5 45 5 39 11 39 11 26 24 26 24 13 37 13 37
49 1 49 1 15 35 15 35 34 16 34 16 5 45 5 45 11 39 11 39 24 26 24 26 37 13 37 13
47 3 47 3 41 9 41 9 22 28 22 28 14 36 14 36 2 48 2 48 31 19 31 19 18 32 18 32
3 47 3 47 9 41 9 41 28 22 28 22 36 14 36 14 48 2 48 2 19 31 19 31 32 18 32 18
47 3 47 3 41 9 41 9 22 28 22 28 14 36 14 36 2 48 2 48 31 19 31 19 18 32 18 32
3 47 3 47 9 41 9 41 28 22 28 22 36 14 36 14 48 2 48 2 19 31 19 31 32 18 32 18
10 40 10 40 4 46 4 46 33 17 33 17 20 30 20 30 43 7 43 7 42 8 42 8 23 27 23 27
40 10 40 10 46 4 46 4 17 33 17 33 30 20 30 20 7 43 7 43 8 42 8 42 27 23 27 23
10 40 10 40 4 46 4 46 33 17 33 17 20 30 20 30 43 7 43 7 42 8 42 8 23 27 23 27
40 10 40 10 46 4 46 4 17 33 17 33 30 20 30 20 7 43 7 43 8 42 8 42 27 23 27 23
21 29 21 29 44 6 44 6 38 12 38 12 25 25 25 25 12 38 12 38 6 44 6 44 29 21 29 21
29 21 29 21 6 44 6 44 12 38 12 38 25 25 25 25 38 12 38 12 44 6 44 6 21 29 21 29
21 29 21 29 44 6 44 6 38 12 38 12 25 25 25 25 12 38 12 38 6 44 6 44 29 21 29 21
29 21 29 21 6 44 6 44 12 38 12 38 25 25 25 25 38 12 38 12 44 6 44 6 21 29 21 29
27 23 27 23 8 42 8 42 7 43 7 43 30 20 30 20 17 33 17 33 46 4 46 4 40 10 40 10
23 27 23 27 42 8 42 8 43 7 43 7 20 30 20 30 33 17 33 17 4 46 4 46 10 40 10 40
27 23 27 23 8 42 8 42 7 43 7 43 30 20 30 20 17 33 17 33 46 4 46 4 40 10 40 10
23 27 23 27 42 8 42 8 43 7 43 7 20 30 20 30 33 17 33 17 4 46 4 46 10 40 10 40
32 18 32 18 19 31 19 31 48 2 48 2 36 14 36 14 28 22 28 22 9 41 9 41 3 47 3 47
18 32 18 32 31 19 31 19 2 48 2 48 14 36 14 36 22 28 22 28 41 9 41 9 47 3 47 3
32 18 32 18 19 31 19 31 48 2 48 2 36 14 36 14 28 22 28 22 9 41 9 41 3 47 3 47
18 32 18 32 31 19 31 19 2 48 2 48 14 36 14 36 22 28 22 28 41 9 41 9 47 3 47 3
37 13 37 13 24 26 24 26 11 39 11 39 5 45 5 45 34 16 34 16 15 35 15 35 49 1 49 1
13 37 13 37 26 24 26 24 39 11 39 11 45 5 45 5 16 34 16 34 35 15 35 15 1 49 1 49
37 13 37 13 24 26 24 26 11 39 11 39 5 45 5 45 34 16 34 16 15 35 15 35 49 1 49 1
13 37 13 37 26 24 26 24 39 11 39 11 45 5 45 5 16 34 16 34 35 15 35 15 1 49 1 49

 

 

+ 64x49x number from third grid of 28x28x28 magic cube [level 1]

0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0

 

 

= 28x28x28 pantriagonal magic cube onsisting of 343x pantriagonal 4x4x4 cube

6 21915 54 21931 2182 19739 2230 19755 966 20955 1014 20971 2822 19099 2870 19115 2438 19483 2486 19499 1606 20315 1654 20331 774 21147 822 21163
21939 46 21891 30 19763 2222 19715 2206 20979 1006 20931 990 19123 2862 19075 2846 19507 2478 19459 2462 20339 1646 20291 1630 21171 814 21123 798
16 21905 64 21921 2192 19729 2240 19745 976 20945 1024 20961 2832 19089 2880 19105 2448 19473 2496 19489 1616 20305 1664 20321 784 21137 832 21153
21945 40 21897 24 19769 2216 19721 2200 20985 1000 20937 984 19129 2856 19081 2840 19513 2472 19465 2456 20345 1640 20297 1624 21177 808 21129 792
2950 18971 2998 18987 2566 19355 2614 19371 1350 20571 1398 20587 838 21083 886 21099 70 21851 118 21867 1926 19995 1974 20011 1094 20827 1142 20843
18995 2990 18947 2974 19379 2606 19331 2590 20595 1390 20547 1374 21107 878 21059 862 21875 110 21827 94 20019 1966 19971 1950 20851 1134 20803 1118
2960 18961 3008 18977 2576 19345 2624 19361 1360 20561 1408 20577 848 21073 896 21089 80 21841 128 21857 1936 19985 1984 20001 1104 20817 1152 20833
19001 2984 18953 2968 19385 2600 19337 2584 20601 1384 20553 1368 21113 872 21065 856 21881 104 21833 88 20025 1960 19977 1944 20857 1128 20809 1112
582 21339 630 21355 198 21723 246 21739 2054 19867 2102 19883 1222 20699 1270 20715 2694 19227 2742 19243 2630 19291 2678 19307 1414 20507 1462 20523
21363 622 21315 606 21747 238 21699 222 19891 2094 19843 2078 20723 1262 20675 1246 19251 2734 19203 2718 19315 2670 19267 2654 20531 1454 20483 1438
592 21329 640 21345 208 21713 256 21729 2064 19857 2112 19873 1232 20689 1280 20705 2704 19217 2752 19233 2640 19281 2688 19297 1424 20497 1472 20513
21369 616 21321 600 21753 232 21705 216 19897 2088 19849 2072 20729 1256 20681 1240 19257 2728 19209 2712 19321 2664 19273 2648 20537 1448 20489 1432
1286 20635 1334 20651 2758 19163 2806 19179 2374 19547 2422 19563 1542 20379 1590 20395 710 21211 758 21227 326 21595 374 21611 1798 20123 1846 20139
20659 1326 20611 1310 19187 2798 19139 2782 19571 2414 19523 2398 20403 1582 20355 1566 21235 750 21187 734 21619 366 21571 350 20147 1838 20099 1822
1296 20625 1344 20641 2768 19153 2816 19169 2384 19537 2432 19553 1552 20369 1600 20385 720 21201 768 21217 336 21585 384 21601 1808 20113 1856 20129
20665 1320 20617 1304 19193 2792 19145 2776 19577 2408 19529 2392 20409 1576 20361 1560 21241 744 21193 728 21625 360 21577 344 20153 1832 20105 1816
1670 20251 1718 20267 454 21467 502 21483 390 21531 438 21547 1862 20059 1910 20075 1030 20891 1078 20907 2886 19035 2934 19051 2502 19419 2550 19435
20275 1710 20227 1694 21491 494 21443 478 21555 430 21507 414 20083 1902 20035 1886 20915 1070 20867 1054 19059 2926 19011 2910 19443 2542 19395 2526
1680 20241 1728 20257 464 21457 512 21473 400 21521 448 21537 1872 20049 1920 20065 1040 20881 1088 20897 2896 19025 2944 19041 2512 19409 2560 19425
20281 1704 20233 1688 21497 488 21449 472 21561 424 21513 408 20089 1896 20041 1880 20921 1064 20873 1048 19065 2920 19017 2904 19449 2536 19401 2520
1990 19931 2038 19947 1158 20763 1206 20779 3014 18907 3062 18923 2246 19675 2294 19691 1734 20187 1782 20203 518 21403 566 21419 134 21787 182 21803
19955 2030 19907 2014 20787 1198 20739 1182 18931 3054 18883 3038 19699 2286 19651 2270 20211 1774 20163 1758 21427 558 21379 542 21811 174 21763 158
2000 19921 2048 19937 1168 20753 1216 20769 3024 18897 3072 18913 2256 19665 2304 19681 1744 20177 1792 20193 528 21393 576 21409 144 21777 192 21793
19961 2024 19913 2008 20793 1192 20745 1176 18937 3048 18889 3032 19705 2280 19657 2264 20217 1768 20169 1752 21433 552 21385 536 21817 168 21769 152
2310 19611 2358 19627 1478 20443 1526 20459 646 21275 694 21291 262 21659 310 21675 2118 19803 2166 19819 902 21019 950 21035 3078 18843 3126 18859
19635 2350 19587 2334 20467 1518 20419 1502 21299 686 21251 670 21683 302 21635 286 19827 2158 19779 2142 21043 942 20995 926 18867 3118 18819 3102
2320 19601 2368 19617 1488 20433 1536 20449 656 21265 704 21281 272 21649 320 21665 2128 19793 2176 19809 912 21009 960 21025 3088 18833 3136 18849
19641 2344 19593 2328 20473 1512 20425 1496 21305 680 21257 664 21689 296 21641 280 19833 2152 19785 2136 21049 936 21001 920 18873 3112 18825 3096

 

 

See for grids and result of 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 5 you use a magic cube of order A and a magic square of order B to construct a magic cube of order AxB. See on this website the construction of:

20x20x20 (pantriagonal)24x24x24 (diagonal)24x24x24 (pantriagonal),

28x28x28 (pantriagonal)30x30x30, (diagonal) and 30x30x30 (pantriagonal)

 

Download
28x28x28, consisting of 343x 4x4x4.xlsx
Microsoft Excel werkblad 1.8 MB