Harvey Heinz found that also non-symmetrical magic squares could be self-complement, if the square has complementary pairs of numbers that are symmetric across either the horizontal or the vertical center line. The resulting complement is either horizontally or vertically reflected.
This order-6 magic square is not symmetrical, but symmetric across the vertical center line and produces a self-complement copy of itself.
1 | 28 | 27 | 10 | 9 | 36 |
35 | 26 | 25 | 12 | 11 | 2 |
3 | 22 | 21 | 16 | 15 | 34 |
33 | 24 | 23 | 14 | 13 | 4 |
20 | 6 | 8 | 29 | 31 | 17 |
19 | 5 | 7 | 30 | 32 | 18 |
36 | 9 | 10 | 27 | 28 | 1 |
2 | 11 | 12 | 25 | 26 | 35 |
34 | 15 | 16 | 21 | 22 | 3 |
4 | 13 | 14 | 23 | 24 | 33 |
17 | 31 | 29 | 8 | 6 | 20 |
18 | 32 | 30 | 7 | 5 | 19 |