### A self-complement magic square of order 9

There is another interesting example of a self-complement magic square on the magic pages of Harvey Heinz. This symmetrical magic square of order n=9 is also composite. It consists of nine order-3 symmetrical magic squares themselves arranged as an order-3 magic square.

 71 64 69 8 1 6 53 46 51 66 68 70 3 5 7 48 50 52 67 72 65 4 9 2 49 54 47 26 19 24 44 37 42 62 55 60 21 23 25 39 41 43 57 59 61 22 27 20 40 45 38 58 63 56 35 28 33 80 73 78 17 10 15 30 32 34 75 77 79 12 14 16 31 36 29 76 81 74 13 18 11
 11 18 13 74 81 76 29 36 31 16 14 12 79 77 75 34 32 30 15 10 17 78 73 80 33 28 35 56 63 58 38 45 40 20 27 22 61 59 57 43 41 39 25 23 21 60 55 62 42 37 44 24 19 26 47 54 49 2 9 4 65 72 67 52 50 48 7 5 3 70 68 66 51 46 53 6 1 8 69 64 71

You will get another symmetrical magic square, which is also self-complement, if you rotate each order-3 square by 90°.

 69 70 65 6 7 2 51 52 47 64 68 72 1 5 9 46 50 54 71 66 67 8 3 4 53 48 49 24 25 20 42 43 38 60 61 56 19 23 27 37 41 45 55 59 63 26 21 22 44 39 40 62 57 58 33 34 29 78 79 74 15 16 11 28 32 36 73 77 81 10 14 18 35 30 31 80 75 76 17 12 13
 13 12 17 76 75 80 31 30 35 18 14 10 81 77 73 36 32 28 11 16 15 74 79 78 29 34 33 58 57 62 40 39 44 22 21 26 63 59 55 45 41 37 27 23 19 56 61 60 38 43 42 20 25 24 49 48 53 4 3 8 67 66 71 54 50 46 9 5 1 72 68 64 47 52 51 2 7 6 65 70 69

And another self-complement symmetrical magic square, if you rotate each order-3 square by 180°.

 65 72 67 2 9 4 47 54 49 70 68 66 7 5 3 52 50 48 69 64 71 6 1 8 51 46 53 20 27 22 38 45 40 56 63 58 25 23 21 43 41 39 61 59 57 24 19 26 42 37 44 60 55 62 29 36 31 74 81 76 11 18 13 34 32 30 79 77 75 16 14 12 33 28 35 78 73 80 15 10 17
 65 72 67 2 9 4 47 54 49 70 68 66 7 5 3 52 50 48 69 64 71 6 1 8 51 46 53 20 27 22 38 45 40 56 63 58 25 23 21 43 41 39 61 59 57 24 19 26 42 37 44 60 55 62 29 36 31 74 81 76 11 18 13 34 32 30 79 77 75 16 14 12 33 28 35 78 73 80 15 10 17

And, easy to guess, also rotations by 270° will produce another self-complement symmetrical magic square.

 67 66 71 4 3 8 49 48 53 72 68 64 9 5 1 54 50 46 65 70 69 2 7 6 47 52 51 22 21 26 40 39 44 58 57 62 27 23 19 45 41 37 63 59 55 20 25 24 38 43 42 56 61 60 31 30 35 76 75 80 13 12 17 36 32 28 81 77 73 18 14 10 29 34 33 74 79 78 11 16 15
 15 16 11 78 79 74 33 34 29 10 14 18 73 77 81 28 32 36 17 12 13 80 75 76 35 30 31 60 61 56 42 43 38 24 25 20 55 59 63 37 41 45 19 23 27 62 57 58 44 39 40 26 21 22 51 52 47 6 7 2 69 70 65 46 50 54 1 5 9 64 68 72 53 48 49 8 3 4 71 66 67