Thank you for this interesting article that mentions the torus construction. You can find more information about magic tori on the pages listed here:
https://carresmagiques.blogspot.fr/
The findings have resulted in a new OEIS sequence:
"Number of magic tori of order n composed of the numbers from 1 to n^2."
https://oeis.org/A270876
which is to be compared with the previous OEIS sequence:
"Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections."
https://oeis.org/A006052

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