[iorrus]

Looks to be related to projective geometry in some way in which every point symmetry has a matching “dual” or line symmetry.

https://en.m.wikipedia.org/wiki/Projective_geometry#Duality

[prof-dr-ir]

It is not. Sorry to disappoint. :)

The "dualities" mentioned in the article are about two seemingly different quantum field theories actually being equivalent. See here, for example:

https://en.wikipedia.org/wiki/S-duality https://en.wikipedia.org/wiki/Seiberg_duality