Use a specific 7x7 magic square and its row- or column grid to construct a 7x7x7 pantriagonal magic cube.

 

First we construct the symmetric (but not pan)magic 7x7 square.

 

 

Take 1x number from first grid

4	5	6	0	1	2	3
5	6	0	1	2	3	4
6	0	1	2	3	4	5
0	1	2	3	4	5	6
1	2	3	4	5	6	0
2	3	4	5	6	0	1
3	4	5	6	0	1	2

 

 

+7x number from second grid (= first grid turned by a quarter to left)

3	4	5	6	0	1	2
2	3	4	5	6	0	1
1	2	3	4	5	6	0
0	1	2	3	4	5	6
6	0	1	2	3	4	5
5	6	0	1	2	3	4
4	5	6	0	1	2	3

 

 

= 7x7 symmetric magic square

26	34	42	43	2	10	18
20	28	29	37	45	4	12
14	15	23	31	39	47	6
1	9	17	25	33	41	49
44	3	11	19	27	35	36
38	46	5	13	21	22	30
32	40	48	7	8	16	24

 

 

We use the 7x7 magic square and its row- or column grid to construct the middle level (4) of the 7x7x7 pantriagonal magic cube. The grids of the remaining levels are horizontal or vertical shifts of level 4. See below the grids and the result.

 

 

Take 1x number from first grid

 

		175	175	175	175	175	175	175
	1
175		44	3	11	19	27	35	36
175		38	46	5	13	21	22	30
175		32	40	48	7	8	16	24
175		26	34	42	43	2	10	18
175		20	28	29	37	45	4	12
175		14	15	23	31	39	47	6
175		1	9	17	25	33	41	49
		175	175	175	175	175	175	175
	2
175		38	46	5	13	21	22	30
175		32	40	48	7	8	16	24
175		26	34	42	43	2	10	18
175		20	28	29	37	45	4	12
175		14	15	23	31	39	47	6
175		1	9	17	25	33	41	49
175		44	3	11	19	27	35	36
		175	175	175	175	175	175	175
	3
175		32	40	48	7	8	16	24
175		26	34	42	43	2	10	18
175		20	28	29	37	45	4	12
175		14	15	23	31	39	47	6
175		1	9	17	25	33	41	49
175		44	3	11	19	27	35	36
175		38	46	5	13	21	22	30
		175	175	175	175	175	175	175
	4
175		26	34	42	43	2	10	18
175		20	28	29	37	45	4	12
175		14	15	23	31	39	47	6
175		1	9	17	25	33	41	49
175		44	3	11	19	27	35	36
175		38	46	5	13	21	22	30
175		32	40	48	7	8	16	24
		175	175	175	175	175	175	175
	5
175		20	28	29	37	45	4	12
175		14	15	23	31	39	47	6
175		1	9	17	25	33	41	49
175		44	3	11	19	27	35	36
175		38	46	5	13	21	22	30
175		32	40	48	7	8	16	24
175		26	34	42	43	2	10	18
		175	175	175	175	175	175	175
	6
175		14	15	23	31	39	47	6
175		1	9	17	25	33	41	49
175		44	3	11	19	27	35	36
175		38	46	5	13	21	22	30
175		32	40	48	7	8	16	24
175		26	34	42	43	2	10	18
175		20	28	29	37	45	4	12
		175	175	175	175	175	175	175
	7
175		1	9	17	25	33	41	49
175		44	3	11	19	27	35	36
175		38	46	5	13	21	22	30
175		32	40	48	7	8	16	24
175		26	34	42	43	2	10	18
175		20	28	29	37	45	4	12
175		14	15	23	31	39	47	6

 

 

+49x number from second grid

 

		21	21	21	21	21	21	21
	1
21		0	1	2	3	4	5	6
21		1	2	3	4	5	6	0
21		2	3	4	5	6	0	1
21		3	4	5	6	0	1	2
21		4	5	6	0	1	2	3
21		5	6	0	1	2	3	4
21		6	0	1	2	3	4	5
	2
21		6	0	1	2	3	4	5
21		0	1	2	3	4	5	6
21		1	2	3	4	5	6	0
21		2	3	4	5	6	0	1
21		3	4	5	6	0	1	2
21		4	5	6	0	1	2	3
21		5	6	0	1	2	3	4
	3
21		5	6	0	1	2	3	4
21		6	0	1	2	3	4	5
21		0	1	2	3	4	5	6
21		1	2	3	4	5	6	0
21		2	3	4	5	6	0	1
21		3	4	5	6	0	1	2
21		4	5	6	0	1	2	3
	4
21		4	5	6	0	1	2	3
21		5	6	0	1	2	3	4
21		6	0	1	2	3	4	5
21		0	1	2	3	4	5	6
21		1	2	3	4	5	6	0
21		2	3	4	5	6	0	1
21		3	4	5	6	0	1	2
	5
21		3	4	5	6	0	1	2
21		4	5	6	0	1	2	3
21		5	6	0	1	2	3	4
21		6	0	1	2	3	4	5
21		0	1	2	3	4	5	6
21		1	2	3	4	5	6	0
21		2	3	4	5	6	0	1
	6
21		2	3	4	5	6	0	1
21		3	4	5	6	0	1	2
21		4	5	6	0	1	2	3
21		5	6	0	1	2	3	4
21		6	0	1	2	3	4	5
21		0	1	2	3	4	5	6
21		1	2	3	4	5	6	0
	7
21		1	2	3	4	5	6	0
21		2	3	4	5	6	0	1
21		3	4	5	6	0	1	2
21		4	5	6	0	1	2	3
21		5	6	0	1	2	3	4
21		6	0	1	2	3	4	5
21		0	1	2	3	4	5	6

 

 

= 7x7x7 pantriagonal magic cube

 

		1204	1204	1204	1204	1204	1204	1204
	1
1204		44	52	109	166	223	280	330
1204		87	144	152	209	266	316	30
1204		130	187	244	252	302	16	73
1204		173	230	287	337	2	59	116
1204		216	273	323	37	94	102	159
1204		259	309	23	80	137	194	202
1204		295	9	66	123	180	237	294
	2
1204		332	46	54	111	168	218	275
1204		32	89	146	154	204	261	318
1204		75	132	189	239	247	304	18
1204		118	175	225	282	339	4	61
1204		161	211	268	325	39	96	104
1204		197	254	311	25	82	139	196
1204		289	297	11	68	125	182	232
	3
1204		277	334	48	56	106	163	220
1204		320	34	91	141	149	206	263
1204		20	77	127	184	241	249	306
1204		63	113	170	227	284	341	6
1204		99	156	213	270	327	41	98
1204		191	199	256	313	27	84	134
1204		234	291	299	13	70	120	177
	4
1204		222	279	336	43	51	108	165
1204		265	322	29	86	143	151	208
1204		308	15	72	129	186	243	251
1204		1	58	115	172	229	286	343
1204		93	101	158	215	272	329	36
1204		136	193	201	258	315	22	79
1204		179	236	293	301	8	65	122
	5
1204		167	224	274	331	45	53	110
1204		210	260	317	31	88	145	153
1204		246	303	17	74	131	188	245
1204		338	3	60	117	174	231	281
1204		38	95	103	160	217	267	324
1204		81	138	195	203	253	310	24
1204		124	181	238	288	296	10	67
	6
1204		112	162	219	276	333	47	55
1204		148	205	262	319	33	90	147
1204		240	248	305	19	76	133	183
1204		283	340	5	62	119	169	226
1204		326	40	97	105	155	212	269
1204		26	83	140	190	198	255	312
1204		69	126	176	233	290	298	12
	7
1204		50	107	164	221	278	335	49
1204		142	150	207	264	321	35	85
1204		185	242	250	307	21	71	128
1204		228	285	342	7	57	114	171
1204		271	328	42	92	100	157	214
1204		314	28	78	135	192	200	257
1204		14	64	121	178	235	292	300

 

 

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)