Simple 3x3x3 magic cube (Composite 1)
The first 'most perfect magic' 3x3x3 cube is published by T. Hugel in 1876 (see website http://members.shaw.ca/hdhcubes/cube_early.htm#Hugel).
Use one of the (including rotating and/or mirroring) eight 3x3
magic squares to construct a 'most perfect magic' 3x3x3 cube. Use a 3x3 magic square as middle (second) level of the first grid. Swap columns to
get the top level and the bottom level of the first grid. To construct the second grid, take the row coordinates (option 1a) or the column coordinates (option 2a) of
level 3 up to 1 (instead of 1 up to 3). It is also possible to swap the numbers 0 and 2 in the second grid (= option 1b and 2b).
[Option 1a]
|
1x grid 1, level 1 |
+9x grid 2, level 1 |
= 3x3x3, level 1 |
||||||||||
|
8 |
6 |
1 |
0 |
1 |
2 |
8 |
15 |
19 |
||||
|
3 |
7 |
5 |
1 |
2 |
0 |
12 |
25 |
5 |
||||
|
4 |
2 |
9 |
2 |
0 |
1 |
22 |
2 |
18 |
||||
|
1x grid 1, level 2 |
+9x grid 2, level 2 |
= 3x3x3, level 2 |
||||||||||
|
6 |
1 |
8 |
2 |
0 |
1 |
24 |
1 |
17 |
||||
|
7 |
5 |
3 |
0 |
1 |
2 |
7 |
14 |
21 |
||||
|
2 |
9 |
4 |
1 |
2 |
0 |
11 |
27 |
4 |
||||
|
1x grid 1, level 3 |
+9x grid 2, level 3 |
= 3x3x3, level 3 |
||||||||||
|
1 |
8 |
6 |
1 |
2 |
0 |
10 |
26 |
6 |
||||
|
5 |
3 |
7 |
2 |
0 |
1 |
23 |
3 |
16 |
||||
|
9 |
4 |
2 |
0 |
1 |
2 |
9 |
13 |
20 |
||||
[Option 1b]
|
1x grid 1, level 1 |
+9x grid 2, level 1 |
= 3x3x3, level 1 |
||||||||||
|
8 |
6 |
1 |
2 |
1 |
0 |
26 |
15 |
1 |
||||
|
3 |
7 |
5 |
1 |
0 |
2 |
12 |
7 |
23 |
||||
|
4 |
2 |
9 |
0 |
2 |
1 |
4 |
20 |
18 |
||||
|
1x grid 1, level 2 |
+9x grid 2, level 2 |
= 3x3x3, level 2 |
||||||||||
|
6 |
1 |
8 |
0 |
2 |
1 |
6 |
19 |
17 |
||||
|
7 |
5 |
3 |
2 |
1 |
0 |
25 |
14 |
3 |
||||
|
2 |
9 |
4 |
1 |
0 |
2 |
11 |
9 |
22 |
||||
|
1x grid 1, level 3 |
+9x grid 2, level 3 |
= 3x3x3, level 3 |
||||||||||
|
1 |
8 |
6 |
1 |
0 |
2 |
10 |
8 |
24 |
||||
|
5 |
3 |
7 |
0 |
2 |
1 |
5 |
21 |
16 |
||||
|
9 |
4 |
2 |
2 |
1 |
0 |
27 |
13 |
2 |
||||
[Option 2a]
|
1x grid 1, level 1 |
+9x grid 2, level 1 |
= 3x3x3, level 1 |
||||||||||
|
8 |
6 |
1 |
0 |
2 |
1 |
8 |
24 |
10 |
||||
|
3 |
7 |
5 |
1 |
0 |
2 |
12 |
7 |
23 |
||||
|
4 |
2 |
9 |
2 |
1 |
0 |
22 |
11 |
9 |
||||
|
1x grid 1, level 2 |
+9x grid 2, level 2 |
= 3x3x3, Level 2 |
||||||||||
|
6 |
1 |
8 |
1 |
0 |
2 |
15 |
1 |
26 |
||||
|
7 |
5 |
3 |
2 |
1 |
0 |
25 |
14 |
3 |
||||
|
2 |
9 |
4 |
0 |
2 |
1 |
2 |
27 |
13 |
||||
|
1x grid 1, Level 3 |
+9x grid 2, level 3 |
= 3x3x3, Level 3 |
||||||||||
|
1 |
8 |
6 |
2 |
1 |
0 |
19 |
17 |
6 |
||||
|
5 |
3 |
7 |
0 |
2 |
1 |
5 |
21 |
16 |
||||
|
9 |
4 |
2 |
1 |
0 |
2 |
18 |
4 |
20 |
||||
[Option 2b]
|
1x grid 1, level 1 |
+9x grid 2, level 1 |
= 3x3x3, level 1 |
||||||||||
|
8 |
6 |
1 |
2 |
0 |
1 |
26 |
6 |
10 |
||||
|
3 |
7 |
5 |
1 |
2 |
0 |
12 |
25 |
5 |
||||
|
4 |
2 |
9 |
0 |
1 |
2 |
4 |
11 |
27 |
||||
|
1x grid 1, level 2 |
+9x grid 2, level 2 |
= 3x3x3, level 2 |
||||||||||
|
6 |
1 |
8 |
1 |
2 |
0 |
15 |
19 |
8 |
||||
|
7 |
5 |
3 |
0 |
1 |
2 |
7 |
14 |
21 |
||||
|
2 |
9 |
4 |
2 |
0 |
1 |
20 |
9 |
13 |
||||
|
1x grid 1, level 3 |
+9x grid 2, level 3 |
= 3x3x3, level 3 |
||||||||||
|
1 |
8 |
6 |
0 |
1 |
2 |
1 |
17 |
24 |
||||
|
5 |
3 |
7 |
2 |
0 |
1 |
23 |
3 |
16 |
||||
|
9 |
4 |
2 |
1 |
2 |
0 |
18 |
22 |
2 |
||||
Magic features:
- In level 2 all rows, columns and main diagonals give the magic sum
- Level 1 and 3 are semi (= simple) magic
- The 9 pilars (e.g. 10+8+24) give the magic sum of 42.
- The 4 space diagonals (e.g. 10+14+18) give the magic sum of 42.
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)
