### Pantriagonal 5x5x5 magic cube (Composite 1)

Use a specific 5x5 magic square and its row- or column grid to construct a 5x5x5 pantriagonal magic cube.

First we construct the 5x5 symmetric (but not pan)magic square.

Take 1x number from first grid

 3 4 0 1 2 4 0 1 2 3 0 1 2 3 4 1 2 3 4 0 2 3 4 0 1

+ 5x number from second grid (= first grid turned a quarter to left)

 2 3 4 0 1 1 2 3 4 0 0 1 2 3 4 4 0 1 2 3 3 4 0 1 2

= 5x5 symmetric magic square

 18 24 5 6 12 22 3 9 15 16 1 7 13 19 25 10 11 17 23 4 14 20 21 2 8

We use the 5x5 magic square and its row- or column grid to construct the middle level (3) of 5x5x5 pantriagonal magic cube. The grids of the remaining levels are horizontal or vertical shifts of the grids of level 3. See below the grids and the result.

Take 1x number from first grid

 65 65 65 65 65 1 65 10 11 17 23 4 65 14 20 21 2 8 65 18 24 5 6 12 65 22 3 9 15 16 65 1 7 13 19 25 65 65 65 65 65 2 65 14 20 21 2 8 65 18 24 5 6 12 65 22 3 9 15 16 65 1 7 13 19 25 65 10 11 17 23 4 65 65 65 65 65 3 65 18 24 5 6 12 65 22 3 9 15 16 65 1 7 13 19 25 65 10 11 17 23 4 65 14 20 21 2 8 65 65 65 65 65 4 65 22 3 9 15 16 65 1 7 13 19 25 65 10 11 17 23 4 65 14 20 21 2 8 65 18 24 5 6 12 65 65 65 65 65 5 65 1 7 13 19 25 65 10 11 17 23 4 65 14 20 21 2 8 65 18 24 5 6 12 65 22 3 9 15 16

+ 25x number from second grid

 10 10 10 10 10 1 10 0 1 2 3 4 10 1 2 3 4 0 10 2 3 4 0 1 10 3 4 0 1 2 10 4 0 1 2 3 10 10 10 10 10 2 10 4 0 1 2 3 10 0 1 2 3 4 10 1 2 3 4 0 10 2 3 4 0 1 10 3 4 0 1 2 10 10 10 10 10 3 10 3 4 0 1 2 10 4 0 1 2 3 10 0 1 2 3 4 10 1 2 3 4 0 10 2 3 4 0 1 10 10 10 10 10 4 10 2 3 4 0 1 10 3 4 0 1 2 10 4 0 1 2 3 10 0 1 2 3 4 10 1 2 3 4 0 10 10 10 10 10 5 10 1 2 3 4 0 10 2 3 4 0 1 10 3 4 0 1 2 10 4 0 1 2 3 10 0 1 2 3 4

= 5x5x5 pantriagonal & symmetric magic cube

 315 315 315 315 315 1 315 10 36 67 98 104 315 39 70 96 102 8 315 68 99 105 6 37 315 97 103 9 40 66 315 101 7 38 69 100 315 315 315 315 315 2 315 114 20 46 52 83 315 18 49 55 81 112 315 47 53 84 115 16 315 51 82 113 19 50 315 85 111 17 48 54 315 315 315 315 315 3 315 93 124 5 31 62 315 122 3 34 65 91 315 1 32 63 94 125 315 35 61 92 123 4 315 64 95 121 2 33 315 315 315 315 315 4 315 72 78 109 15 41 315 76 107 13 44 75 315 110 11 42 73 79 315 14 45 71 77 108 315 43 74 80 106 12 315 315 315 315 315 5 315 26 57 88 119 25 315 60 86 117 23 29 315 89 120 21 27 58 315 118 24 30 56 87 315 22 28 59 90 116

See for check if all numbers are in the magic cube and addition of the numbers give the right magic sum, the download below.

With method composite 1 you use a magic square to construct a magic cube. See on this website the construction of:

5x5x5, pantriagonal.xlsx