The ellipse associated with the Ring Dupin Cyclide is easy to make with MoI's ellipse command.
The center is the origin, and the two radii are the aRadius and bRadius = sqrt(aRadius*aRadius - cRadius*cRadius).
A checkbox for this may be added. Points on the ellipse are center points for spheres caged by the scaffolding network.
These spheres correspond to circles in the Top View, xy plane.
There are rendered images of tangent caged spheres on the internet. Making the spheres/circles tangent to each other seems to be trial and error?
An offset radius for the scaffolding network would permit the network to be wires of diameter twice the offset radius.

- Brian