### Ultra magic 25x25x25 cube

Use an ultramagic 5x5 square to construct a 25x25x25 cube which is Nasik, symmetric and 5x5@ compact.

@ The ultra magic 25x25x25 cube is 5x5 compact in each level, so the cube is also 5x5x5 compact. The cube is also 5x5 compact vertical through the levels. But the cube is not 5x5 compact horizontal through the levels. I believe it is not possible to construct a magic 25x25x25 cube which is Nasik, symmetric and 5x5 compact in all 3 (instead of 2 of the 3) directions.

(1) Put the 5 rows of the ultra magic 5x5 square next to each other to construct the first row of the first grid of the 13th level of the 25x25x25 cube. Construct row 2 up to 25 of the first grid of the 13th level of the 25x25x25 magic cube by shifting the first row each time 5 places to the right.

(2) The second grid is an reflection (= rotated and mirrored) of the first grid.

(3) The first and second grid in the remaing levels are the shifted versions of the first and second grid of the 13th level: 2-4-6-8-10-12-14-16-18-20-22-24-1-3-5-7-9-11-13-15-17-19-21-23.

(4) Take as third grid, the first grid, but put the levels in reversed order (25 up to 1 instead of 1 up to 25). Take 625x number from third grid.

Take number+1 from the first grid of the 13th level of the 25x25x25 magic cube

 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 0 22 9 13 16 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 14 18 1 20 7 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 21 5 12 19 3 17 4 23 6 10 8 11 15 2 24 0 22 9 13 16 14 18 1 20 7

+ 25x number from the second grid of the 13th level of the 25x25x25 magic cube

 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 21 17 8 0 14 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 5 4 11 22 18 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 12 23 15 9 1 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 19 6 2 13 20 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7 3 10 24 16 7

See all grids and all levels of the 25x25x25 magic cube in the download below.

25x25x25, Ultra magic 25x25x25 cube, gri