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:

3x3x3 (simple),  4x4x4 (most perfect), 5x5x5 (pantriagonal), 7x7x7 (pantriagonal),

9x9x9 (pandiagonal & compact), 12x12x12 (diagonal), 12x12x12 (pantriagonal),

15x15x15 (pandiagonal & compact), 16x16x16 (Nasik)a, 16x16x16 (Nasik)b,

20x20x20 (diagonal), 20x20x20 (pantriagonal), 24x24x24 (diagonal), 24x24x24

(pantriagonal), 28x28x28 (diagonal), 28x28x28 (pantriagonal)