16x16x16x16 most perfect magic hypercube
With the help of Dwane Campbell I have constructed a most perfect 16x16x16x16 magic hypercube. Each 1/4 row/column/pillar/post gives 1/4 of the magic sum and each 1/2 diagonal in the levels gives 1/2 of the magic sum. The 16x16x16x16 magic cube is 2x2 compact in all 3 directions.
I used 4 grids with the numbers 1 up to 16 in it to construct a most perfect 16x16x16x16 magic cube.
See below the structure of the first grid of the 16x16x16x16 magic cube:
Top level of the first four 16x16x16 sub-cubes of the first grid of the 16x16x16x16 cube
Grid A1
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
|
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
|
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
|
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
|
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
|
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
|
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
|
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
|
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
|
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
|
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
|
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
|
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
|
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
Grid A2
|
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
|
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
|
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
|
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
|
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
|
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
|
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
|
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
|
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
|
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
|
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
|
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
|
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
Grid A3
|
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
|
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
|
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
|
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
|
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
|
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
|
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
|
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
|
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
|
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
|
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
|
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
|
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
Grid A4
|
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
|
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
|
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
|
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
|
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
|
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
|
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
|
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
5 |
12 |
|
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
4 |
13 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
|
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
2 |
15 |
|
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
7 |
10 |
|
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
11 |
6 |
|
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
14 |
3 |
The sequence of the 16x16 levels of the first grid of the 16x16x16x16 cube is:
A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’
A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’
A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4
A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2
A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’
A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’
A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4
A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2
A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’
A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’
A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A
A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2
A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’
A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’
A1’ A2’ A3’ A4’ A1 A2 A3 A4 A1’ A2’ A3’ A4’ A1 A2 A3 A4
A3’ A4’ A1’ A2’ A3 A4 A1 A2 A3’ A4’ A1’ A2’ A3 A4 A1 A2
' = inverse
See below the structure of the second grid of the 16x16x16x16 magic cube:
Top level of the first four 16x16x16 sub-cubes of the second grid of the 16x16x16x16 cube
Grid B1
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
Grid B2
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
|
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
|
16 |
9 |
2 |
7 |
11 |
14 |
5 |
4 |
1 |
8 |
15 |
10 |
6 |
3 |
12 |
13 |
Grid B3
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
|
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
|
11 |
14 |
5 |
4 |
16 |
9 |
2 |
7 |
6 |
3 |
12 |
13 |
1 |
8 |
15 |
10 |
Grid B4
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
|
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
|
5 |
4 |
16 |
9 |
2 |
7 |
11 |
14 |
12 |
13 |
1 |
8 |
15 |
10 |
6 |
3 |
The sequence of the 16x16 levels of the first grid of the 16x16x16x16 cube is:
B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’
B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’
B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’
B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’
B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3
B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4
B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1
B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2
B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’
B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’
B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’
B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’
B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3 B1’ B3’ B1 B3
B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4 B2’ B4’ B2 B4
B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1 B3’ B1’ B3 B1
B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2 B4’ B2’ B4 B2
See below the structure of the third grid of the 16x16x16x16 magic cube:
Top level of the first 16x16x16 sub-cube of the third grid of the 16x16x16x16 cube
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
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1 |
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1 |
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1 |
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|
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
|
1 |
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1 |
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1 |
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1 |
|
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
|
1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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|
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1 |
16 |
1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
|
1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
16 |
1 |
16 |
1 |
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1 |
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1 |
16 |
1 |
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1 |
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1 |
|
1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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|
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1 |
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1 |
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1 |
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1 |
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1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
All levels have the same structure with in the top left corner the number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, respectively 16 in the following sequence:
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
01-08-13-12 15-10-03-06 16-09-04-05 02-07-14-11
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
16-09-04-05 02-07-14-11 01-08-13-12 15-10-03-06
See below the structure of the fourth grid of the 16x16x16x16 magic cube:
Top level of the first 16x16x16 sub-cube of the fourth grid of the 16x16x16x16 cube
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
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|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
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1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
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1 |
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1 |
|
1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
|
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
16 |
1 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
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1 |
16 |
1 |
16 |
1 |
16 |
|
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1 |
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1 |
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1 |
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1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
|
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
1 |
16 |
The fourth grid has the same structure as the third grid!!!
All levels have the same structure with in the top left corner the digit 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, respectively 16 in the following sequence:
01-01-16-16 01-01-16-16 01-01-16-16 01-01-16-16
08-08-09-09 08-08-09-09 08-08-09-09 08-08-09-09
13-13-04-04 13-13-04-04 13-13-04-04 13-13-04-04
12-12-05-05 12-12-05-05 12-12-05-05 12-12-05-05
15-15-02-02 15-15-02-02 15-15-02-02 15-15-02-02
10-10-07-07 10-10-07-07 10-10-07-07 10-10-07-07
03-03-14-14 03-03-14-14 03-03-14-14 03-03-14-14
06-06-11-11 06-06-11-11 06-06-11-11 06-06-11-11
16-16-01-01 16-16-01-01 16-16-01-01 16-16-01-01
09-09-08-08 09-09-08-08 09-09-08-08 09-09-08-08
04-04-13-13 04-04-13-13 04-04-13-13 04-04-13-13
05-05-12-12 05-05-12-12 05-05-12-12 05-05-12-12
02-02-15-15 02-02-15-15 02-02-15-15 02-02-15-15
07-07-10-10 07-07-10-10 07-07-10-10 07-07-10-10
14-14-03-03 14-14-03-03 14-14-03-03 14-14-03-03
11-11-06-06 11-11-06-06 11-11-06-06 11-11-06-06
See the result and all grids in the download below.
Dwane Campbell constructed a 16x16x16x16 magic cube which is Nasik and each 1/4 row/column/diagonal (in the levels) and 1/4 pillar/post/space diagonal gives 1/4 of the magic sum. This 16x16x16x16 magic cube is not 2x2 compact. See an analysis of Dwane Campell's 16x16x16x16 magic cube in the download below.