Most perfect 4x4x4 magic cube (Composite 1)
See below how to use a 4x4 panmagic square to construct a most perfect 4x4x4 magic cube:
|
1x number |
+ 4x number |
= |
first level 4x4x4 cube |
|||||||||||||
|
1 |
8 |
13 |
12 |
1 |
0 |
3 |
2 |
17 |
8 |
61 |
44 |
|||||
|
15 |
10 |
3 |
6 |
0 |
2 |
1 |
3 |
15 |
42 |
19 |
54 |
|||||
|
4 |
5 |
16 |
9 |
3 |
1 |
2 |
0 |
52 |
21 |
48 |
9 |
|||||
|
14 |
11 |
2 |
7 |
2 |
3 |
0 |
1 |
46 |
59 |
2 |
23 |
|||||
|
1x number |
+ 4x number |
= |
second level 4x4x4 cube |
|||||||||||||
|
10 |
15 |
6 |
3 |
0 |
2 |
1 |
3 |
10 |
47 |
22 |
51 |
|||||
|
8 |
1 |
12 |
13 |
2 |
3 |
0 |
1 |
40 |
49 |
12 |
29 |
|||||
|
11 |
14 |
7 |
2 |
1 |
0 |
3 |
2 |
27 |
14 |
55 |
34 |
|||||
|
5 |
4 |
9 |
16 |
3 |
1 |
2 |
0 |
53 |
20 |
41 |
16 |
|||||
|
1x number |
+ 4x number |
= |
third level 4x4x4 cube |
|||||||||||||
|
16 |
9 |
4 |
5 |
3 |
1 |
2 |
0 |
64 |
25 |
36 |
5 |
|||||
|
2 |
7 |
14 |
11 |
1 |
0 |
3 |
2 |
18 |
7 |
62 |
43 |
|||||
|
13 |
12 |
1 |
8 |
2 |
3 |
0 |
1 |
45 |
60 |
1 |
24 |
|||||
|
3 |
6 |
15 |
10 |
0 |
2 |
1 |
3 |
3 |
38 |
31 |
58 |
|||||
|
1x number |
+ 4x number |
= |
fourth level 4x4x4 cube |
|||||||||||||
|
7 |
2 |
11 |
14 |
2 |
3 |
0 |
1 |
39 |
50 |
11 |
30 |
|||||
|
9 |
16 |
5 |
4 |
3 |
1 |
2 |
0 |
57 |
32 |
37 |
4 |
|||||
|
6 |
3 |
10 |
15 |
0 |
2 |
1 |
3 |
6 |
35 |
26 |
63 |
|||||
|
12 |
13 |
8 |
1 |
1 |
0 |
3 |
2 |
28 |
13 |
56 |
33 |
|||||
In the levels all rows/columns/diagonals give the magic sum and through the levels all pillars and diagonals (from left to right, right to left, top to bottom and bottom to top) give the magic sum. The space diagonals don't give the magic sum (so the most perfect 4x4x4 magic cube is only semi magic).
N.B.: Use instead of a panmagic 4x4 square (= group 1) a symmetric 4x4 square (= group 3; Dürer magic) or the vertical oriented magic 4x4 squares from group 6 to construct a most perfect 4x4x4 magic cube; see download below.
With method composite 1 you use a magic square to construct a magic cube. See on this website the construction of:
3x3x3 (simple), 4x4x4 (most perfect), 5x5x5 (pantriagonal), 7x7x7 (pantriagonal),
9x9x9 (pandiagonal & compact), 12x12x12 (diagonal), 12x12x12 (pantriagonal),
15x15x15 (pandiagonal & compact), 16x16x16 (Nasik)a, 16x16x16 (Nasik)b,
20x20x20 (diagonal), 20x20x20 (pantriagonal), 24x24x24 (diagonal), 24x24x24
(pantriagonal), 28x28x28 (diagonal), 28x28x28 (pantriagonal)
