Midpoints Between Many Different Points (in groups of four)

Sorry for the confusing title. What I'm trying to do, is to get the points among 4 different points, but in a large group of points, in the positions (but not limited) of the GREEN rings drawn below:

That's in order to add a torus facing the other direction, creating a chainmail like the one below:

Any help or suggestions is much appreciated, see .gh file attached. :)