Scherk minimal surface increase nodes

Hello, I was wondering if you could give me some advice on how I should approach making scherk minimal surface (saddle tower).

I was able to make the base scherk surface mesh without using plugins… however, i am not sure how to increase the frequency of the saddles by k-set, as demonstrated by Hermann Karcher and some recent papers by Laura Nica, (see the attached image)

does anyone have an idea on how do resolve this?

for more information look into: (21.1 KB)

what I understand is that you want to change the symmetry. This is not too difficult for the general case, you represent your mesh in cylindrical coordinates then knowing the polar angle and the first symmetry you apply some transformation. The problem is to keep good connectivity, some faces are crossing symmetry plan. SO mesh must be cut first or you apply the tool on points.