Half pandiagonal 5x5x5 magic cube (Shift method)

See on www.trump.de/magic-squares/magic-cubes/cubes-1.html the following diagonal magic 5x5x5 cube.

The first known perfect magic cube of order 5

Walter Trump and Christian Boyer, 2003-11-13

This 5x5x5 magic cube has as magic features:

the 5 rows, the 5 columns and the 2 diagonals in each level give the magic sum of 315;
the 25 pilars give the magic sum of 315;
the 20 diagonals through the 5 levels give the magic sum of 315 (e.g. 115+64+38+87+11=315 or 106+44+58+87+20=315);
the 4 tridiagonals give the magic sum of 315 (e.g. 67+39+63+87+59=315).

Use the same method to construct the panmagic 5x5 square (shift) to construct a symmetric & semi panmagic 5x5x5 cube.

Choose as first row of the first grid in the first level: 2-3-4-0-1. Construct row 2 up to 5 of the first grid of the first level by shifting the first row each time 2 places to the left. Construct the first grid of level 2 up to 5 by shifting the columns of the first grid of the first level each time 2 places to the left.

Choose as first row of the second grid in the first level: 0-1-2-3-4. Construct row 2 up to 5 of the second grid of the first level by shifting the first row each time 2 places to the right. Construct the second grid of level 2 up to 5 by shifting the columns of the second grid of the first level each time 2 places to the left.

The third grid is the same as the second grid, but the levels must be put in reversed order (5 up to 1 instead of 1 up to 5).

Take 1x number from first grid + 5x number from second grid + 25x number from third grid to get a symmetric & semi (pan)magic 5x5x5 cube.

*1x number +1 + 5x number + 25x number = 5x5x5 cube, first level*
2	3	4	0	1	0	1	2	3	4	3	4	0	1	2	78	109	15	41	72
4	0	1	2	3	3	4	0	1	2	1	2	3	4	0	45	71	77	108	14
1	2	3	4	0	1	2	3	4	0	4	0	1	2	3	107	13	44	75	76
3	4	0	1	2	4	0	1	2	3	2	3	4	0	1	74	80	106	12	43
0	1	2	3	4	2	3	4	0	1	0	1	2	3	4	11	42	73	79	110


1x number +1 + 5x number + 25x number = 5x5x5 cube, second level
4	0	1	2	3	2	3	4	0	1	1	2	3	4	0	40	66	97	103	9
1	2	3	4	0	0	1	2	3	4	4	0	1	2	3	102	8	39	70	96
3	4	0	1	2	3	4	0	1	2	2	3	4	0	1	69	100	101	7	38
0	1	2	3	4	1	2	3	4	0	0	1	2	3	4	6	37	68	99	105
2	3	4	0	1	4	0	1	2	3	3	4	0	1	2	98	104	10	36	67


1x number +1 + 5x number + 25x number = 5x5x5 cube, third level
1	2	3	4	0	4	0	1	2	3	4	0	1	2	3	122	3	34	65	91
3	4	0	1	2	2	3	4	0	1	2	3	4	0	1	64	95	121	2	33
0	1	2	3	4	0	1	2	3	4	0	1	2	3	4	1	32	63	94	125
2	3	4	0	1	3	4	0	1	2	3	4	0	1	2	93	124	5	31	62
4	0	1	2	3	1	2	3	4	0	1	2	3	4	0	35	61	92	123	4


1x nmber +1 + 5x number + 25x number = 5x5x5 cube, fourth level
3	4	0	1	2	1	2	3	4	0	2	3	4	0	1	59	90	116	22	28
0	1	2	3	4	4	0	1	2	3	0	1	2	3	4	21	27	58	89	120
2	3	4	0	1	2	3	4	0	1	3	4	0	1	2	88	119	25	26	57
4	0	1	2	3	0	1	2	3	4	1	2	3	4	0	30	56	87	118	24
1	2	3	4	0	3	4	0	1	2	4	0	1	2	3	117	23	29	60	86


1x number +1 + 5x number + 25x number = 5x5x5 cube, fifth level
0	1	2	3	4	3	4	0	1	2	0	1	2	3	4	16	47	53	84	115
2	3	4	0	1	1	2	3	4	0	3	4	0	1	2	83	114	20	46	52
4	0	1	2	3	4	0	1	2	3	1	2	3	4	0	50	51	82	113	19
1	2	3	4	0	2	3	4	0	1	4	0	1	2	3	112	18	49	55	81
3	4	0	1	2	0	1	2	3	4	2	3	4	0	1	54	85	111	17	48

Less & extra magic features:

The vertical diagonals through the levels give not the magic sum;
The pandiagonals in each level give the magic sum of 315;
The horizontal pandiagonals through the levels give the magic sum of 315

Use the shift method to construct magic cubes of odd order and from 9x9x9 and up the result is Nasik. See on this website the shift method for:

5x5x5, 7x7x7, 9x9x9, 11x11x11, 13x13x13, 15x15x15, 17x17x17, 19x19x19, 21x21x21,

23x23x23, 25x25x25, 27x27x27, 29x29x29, 31x31x31

5x5x5, semi [pan]magic 5x5x5 cube.xls

Microsoft Excel werkblad 80.5 KB

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See below a download with the analysis of Walter Trump & Christian Boyer's 5x5x5 magic cube and notify that the grids are irregular.

5x5x5, diagonal, analysis.xlsx

Microsoft Excel werkblad 30.8 KB

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5x5x5 magic cube