Pantriagonal 24x24x24 magic cube (Composite 5')
Use a 3x3x3 magic cube and it's inverse and a 8x8 most perfect square to construct a pantriagonal 24x24x24 magic cube.
The first grid consists of 768x a 3x3x3 magic cube and 768x it's inverse.
The second grid consists of a 3x3 'blown up' most perfect 8x8 magic square and it's inverse.
The third grid consists of the numbers 0 up to 7.
See below the construction of level 1.
Take 1x number from first grid with 3x3x3 magic cube and it's inverse [level 1]
|
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
|
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
|
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
|
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
|
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
|
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
|
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
|
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
|
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
|
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
|
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
|
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
|
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
|
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
|
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
|
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
|
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
|
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
|
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
|
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
|
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
|
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
20 |
13 |
9 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
8 |
15 |
19 |
|
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
16 |
3 |
23 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
12 |
25 |
5 |
|
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
6 |
26 |
10 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
22 |
2 |
18 |
+27x number from second grid with 3x3x3 'blown up' most perfect 8x8 magic square [level 1]
|
1 |
1 |
1 |
60 |
60 |
60 |
22 |
22 |
22 |
47 |
47 |
47 |
2 |
2 |
2 |
59 |
59 |
59 |
21 |
21 |
21 |
48 |
48 |
48 |
|
1 |
1 |
1 |
60 |
60 |
60 |
22 |
22 |
22 |
47 |
47 |
47 |
2 |
2 |
2 |
59 |
59 |
59 |
21 |
21 |
21 |
48 |
48 |
48 |
|
1 |
1 |
1 |
60 |
60 |
60 |
22 |
22 |
22 |
47 |
47 |
47 |
2 |
2 |
2 |
59 |
59 |
59 |
21 |
21 |
21 |
48 |
48 |
48 |
|
56 |
56 |
56 |
13 |
13 |
13 |
35 |
35 |
35 |
26 |
26 |
26 |
55 |
55 |
55 |
14 |
14 |
14 |
36 |
36 |
36 |
25 |
25 |
25 |
|
56 |
56 |
56 |
13 |
13 |
13 |
35 |
35 |
35 |
26 |
26 |
26 |
55 |
55 |
55 |
14 |
14 |
14 |
36 |
36 |
36 |
25 |
25 |
25 |
|
56 |
56 |
56 |
13 |
13 |
13 |
35 |
35 |
35 |
26 |
26 |
26 |
55 |
55 |
55 |
14 |
14 |
14 |
36 |
36 |
36 |
25 |
25 |
25 |
|
43 |
43 |
43 |
18 |
18 |
18 |
64 |
64 |
64 |
5 |
5 |
5 |
44 |
44 |
44 |
17 |
17 |
17 |
63 |
63 |
63 |
6 |
6 |
6 |
|
43 |
43 |
43 |
18 |
18 |
18 |
64 |
64 |
64 |
5 |
5 |
5 |
44 |
44 |
44 |
17 |
17 |
17 |
63 |
63 |
63 |
6 |
6 |
6 |
|
43 |
43 |
43 |
18 |
18 |
18 |
64 |
64 |
64 |
5 |
5 |
5 |
44 |
44 |
44 |
17 |
17 |
17 |
63 |
63 |
63 |
6 |
6 |
6 |
|
30 |
30 |
30 |
39 |
39 |
39 |
9 |
9 |
9 |
52 |
52 |
52 |
29 |
29 |
29 |
40 |
40 |
40 |
10 |
10 |
10 |
51 |
51 |
51 |
|
30 |
30 |
30 |
39 |
39 |
39 |
9 |
9 |
9 |
52 |
52 |
52 |
29 |
29 |
29 |
40 |
40 |
40 |
10 |
10 |
10 |
51 |
51 |
51 |
|
30 |
30 |
30 |
39 |
39 |
39 |
9 |
9 |
9 |
52 |
52 |
52 |
29 |
29 |
29 |
40 |
40 |
40 |
10 |
10 |
10 |
51 |
51 |
51 |
|
3 |
3 |
3 |
58 |
58 |
58 |
24 |
24 |
24 |
45 |
45 |
45 |
4 |
4 |
4 |
57 |
57 |
57 |
23 |
23 |
23 |
46 |
46 |
46 |
|
3 |
3 |
3 |
58 |
58 |
58 |
24 |
24 |
24 |
45 |
45 |
45 |
4 |
4 |
4 |
57 |
57 |
57 |
23 |
23 |
23 |
46 |
46 |
46 |
|
3 |
3 |
3 |
58 |
58 |
58 |
24 |
24 |
24 |
45 |
45 |
45 |
4 |
4 |
4 |
57 |
57 |
57 |
23 |
23 |
23 |
46 |
46 |
46 |
|
54 |
54 |
54 |
15 |
15 |
15 |
33 |
33 |
33 |
28 |
28 |
28 |
53 |
53 |
53 |
16 |
16 |
16 |
34 |
34 |
34 |
27 |
27 |
27 |
|
54 |
54 |
54 |
15 |
15 |
15 |
33 |
33 |
33 |
28 |
28 |
28 |
53 |
53 |
53 |
16 |
16 |
16 |
34 |
34 |
34 |
27 |
27 |
27 |
|
54 |
54 |
54 |
15 |
15 |
15 |
33 |
33 |
33 |
28 |
28 |
28 |
53 |
53 |
53 |
16 |
16 |
16 |
34 |
34 |
34 |
27 |
27 |
27 |
|
41 |
41 |
41 |
20 |
20 |
20 |
62 |
62 |
62 |
7 |
7 |
7 |
42 |
42 |
42 |
19 |
19 |
19 |
61 |
61 |
61 |
8 |
8 |
8 |
|
41 |
41 |
41 |
20 |
20 |
20 |
62 |
62 |
62 |
7 |
7 |
7 |
42 |
42 |
42 |
19 |
19 |
19 |
61 |
61 |
61 |
8 |
8 |
8 |
|
41 |
41 |
41 |
20 |
20 |
20 |
62 |
62 |
62 |
7 |
7 |
7 |
42 |
42 |
42 |
19 |
19 |
19 |
61 |
61 |
61 |
8 |
8 |
8 |
|
32 |
32 |
32 |
37 |
37 |
37 |
11 |
11 |
11 |
50 |
50 |
50 |
31 |
31 |
31 |
38 |
38 |
38 |
12 |
12 |
12 |
49 |
49 |
49 |
|
32 |
32 |
32 |
37 |
37 |
37 |
11 |
11 |
11 |
50 |
50 |
50 |
31 |
31 |
31 |
38 |
38 |
38 |
12 |
12 |
12 |
49 |
49 |
49 |
|
32 |
32 |
32 |
37 |
37 |
37 |
11 |
11 |
11 |
50 |
50 |
50 |
31 |
31 |
31 |
38 |
38 |
38 |
12 |
12 |
12 |
49 |
49 |
49 |
+27x64x number from third grid with numbers 0 up to 7 [level 1]
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
|
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
7 |
7 |
7 |
0 |
0 |
0 |
= pantriagonal 24x24x24 magic cube [level 1]
|
8 |
15 |
19 |
13697 |
13704 |
13708 |
575 |
582 |
586 |
13346 |
13353 |
13357 |
47 |
40 |
36 |
13682 |
13675 |
13671 |
560 |
553 |
549 |
13385 |
13378 |
13374 |
|
12 |
25 |
5 |
13701 |
13714 |
13694 |
579 |
592 |
572 |
13350 |
13363 |
13343 |
43 |
30 |
50 |
13678 |
13665 |
13685 |
556 |
543 |
563 |
13381 |
13368 |
13388 |
|
22 |
2 |
18 |
13711 |
13691 |
13707 |
589 |
569 |
585 |
13360 |
13340 |
13356 |
33 |
53 |
37 |
13668 |
13688 |
13672 |
546 |
566 |
550 |
13371 |
13391 |
13375 |
|
13589 |
13596 |
13600 |
332 |
339 |
343 |
13022 |
13029 |
13033 |
683 |
690 |
694 |
13574 |
13567 |
13563 |
371 |
364 |
360 |
13061 |
13054 |
13050 |
668 |
661 |
657 |
|
13593 |
13606 |
13586 |
336 |
349 |
329 |
13026 |
13039 |
13019 |
687 |
700 |
680 |
13570 |
13557 |
13577 |
367 |
354 |
374 |
13057 |
13044 |
13064 |
664 |
651 |
671 |
|
13603 |
13583 |
13599 |
346 |
326 |
342 |
13036 |
13016 |
13032 |
697 |
677 |
693 |
13560 |
13580 |
13564 |
357 |
377 |
361 |
13047 |
13067 |
13051 |
654 |
674 |
658 |
|
1154 |
1147 |
1143 |
12575 |
12568 |
12564 |
1721 |
1714 |
1710 |
12224 |
12217 |
12213 |
1169 |
1176 |
1180 |
12536 |
12543 |
12547 |
1682 |
1689 |
1693 |
12239 |
12246 |
12250 |
|
1150 |
1137 |
1157 |
12571 |
12558 |
12578 |
1717 |
1704 |
1724 |
12220 |
12207 |
12227 |
1173 |
1186 |
1166 |
12540 |
12553 |
12533 |
1686 |
1699 |
1679 |
12243 |
12256 |
12236 |
|
1140 |
1160 |
1144 |
12561 |
12581 |
12565 |
1707 |
1727 |
1711 |
12210 |
12230 |
12214 |
1183 |
1163 |
1179 |
12550 |
12530 |
12546 |
1696 |
1676 |
1692 |
12253 |
12233 |
12249 |
|
12899 |
12892 |
12888 |
1046 |
1039 |
1035 |
12332 |
12325 |
12321 |
1397 |
1390 |
1386 |
12860 |
12867 |
12871 |
1061 |
1068 |
1072 |
12347 |
12354 |
12358 |
1358 |
1365 |
1369 |
|
12895 |
12882 |
12902 |
1042 |
1029 |
1049 |
12328 |
12315 |
12335 |
1393 |
1380 |
1400 |
12864 |
12877 |
12857 |
1065 |
1078 |
1058 |
12351 |
12364 |
12344 |
1362 |
1375 |
1355 |
|
12885 |
12905 |
12889 |
1032 |
1052 |
1036 |
12318 |
12338 |
12322 |
1383 |
1403 |
1387 |
12874 |
12854 |
12870 |
1075 |
1055 |
1071 |
12361 |
12341 |
12357 |
1372 |
1352 |
1368 |
|
62 |
69 |
73 |
13643 |
13650 |
13654 |
629 |
636 |
640 |
13292 |
13299 |
13303 |
101 |
94 |
90 |
13628 |
13621 |
13617 |
614 |
607 |
603 |
13331 |
13324 |
13320 |
|
66 |
79 |
59 |
13647 |
13660 |
13640 |
633 |
646 |
626 |
13296 |
13309 |
13289 |
97 |
84 |
104 |
13624 |
13611 |
13631 |
610 |
597 |
617 |
13327 |
13314 |
13334 |
|
76 |
56 |
72 |
13657 |
13637 |
13653 |
643 |
623 |
639 |
13306 |
13286 |
13302 |
87 |
107 |
91 |
13614 |
13634 |
13618 |
600 |
620 |
604 |
13317 |
13337 |
13321 |
|
13535 |
13542 |
13546 |
386 |
393 |
397 |
12968 |
12975 |
12979 |
737 |
744 |
748 |
13520 |
13513 |
13509 |
425 |
418 |
414 |
13007 |
13000 |
12996 |
722 |
715 |
711 |
|
13539 |
13552 |
13532 |
390 |
403 |
383 |
12972 |
12985 |
12965 |
741 |
754 |
734 |
13516 |
13503 |
13523 |
421 |
408 |
428 |
13003 |
12990 |
13010 |
718 |
705 |
725 |
|
13549 |
13529 |
13545 |
400 |
380 |
396 |
12982 |
12962 |
12978 |
751 |
731 |
747 |
13506 |
13526 |
13510 |
411 |
431 |
415 |
12993 |
13013 |
12997 |
708 |
728 |
712 |
|
1100 |
1093 |
1089 |
12629 |
12622 |
12618 |
1667 |
1660 |
1656 |
12278 |
12271 |
12267 |
1115 |
1122 |
1126 |
12590 |
12597 |
12601 |
1628 |
1635 |
1639 |
12293 |
12300 |
12304 |
|
1096 |
1083 |
1103 |
12625 |
12612 |
12632 |
1663 |
1650 |
1670 |
12274 |
12261 |
12281 |
1119 |
1132 |
1112 |
12594 |
12607 |
12587 |
1632 |
1645 |
1625 |
12297 |
12310 |
12290 |
|
1086 |
1106 |
1090 |
12615 |
12635 |
12619 |
1653 |
1673 |
1657 |
12264 |
12284 |
12268 |
1129 |
1109 |
1125 |
12604 |
12584 |
12600 |
1642 |
1622 |
1638 |
12307 |
12287 |
12303 |
|
12953 |
12946 |
12942 |
992 |
985 |
981 |
12386 |
12379 |
12375 |
1343 |
1336 |
1332 |
12914 |
12921 |
12925 |
1007 |
1014 |
1018 |
12401 |
12408 |
12412 |
1304 |
1311 |
1315 |
|
12949 |
12936 |
12956 |
988 |
975 |
995 |
12382 |
12369 |
12389 |
1339 |
1326 |
1346 |
12918 |
12931 |
12911 |
1011 |
1024 |
1004 |
12405 |
12418 |
12398 |
1308 |
1321 |
1301 |
|
12939 |
12959 |
12943 |
978 |
998 |
982 |
12372 |
12392 |
12376 |
1329 |
1349 |
1333 |
12928 |
12908 |
12924 |
1021 |
1001 |
1017 |
12415 |
12395 |
12411 |
1318 |
1298 |
1314 |
N.B.: In the pantriagonal magic cube 1/2 rows/columns/pillars give 1/2 of the magic sum.
See in the download below the construction of all levels, check if all formulas give the valid magic sum and check if all numbers are in the magic cube.
With method composite 5' you use a 3x3x3 magic cube and its inverse and a 4x4 panmagic square or a most perfect 8x8 magic square to construct a pantriagonal magic cube. See on this website the construction of:
