5x5x5 pantriagonal magic cube

 

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.

 

Download
5x5x5, pantriagonal.xlsx
Microsoft Excel werkblad 31.1 KB