Symmetric transformation

Marios Mamzeris shows us that you can transform a odd square with sequencial numbers into a symmetric magic square in two steps (https://www.oddmagicsquares.com/):

Step 1, horizontal swap

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

Step 2, vertical swap

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

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31

7x7, symmetric transformation.xlsx

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7x7 magic square