Hi Petras,
The pairs of cylinders to keep in contact came simply by pairing each halfedge with its next.
For the axis to rotate about I used a line through the midpoint of the edge in the direction of the average of the normals of the 2 adjacent faces (I guess if you are using general polygons the normal is not so uniquely defined as with triangles, but I think any estimate should work here).
This part is similar to what Tomohiro Tachi used for generating tensegrity structures in this paper:
As for the over/under - yes it’s true that this approach doesn’t always result in all sticks resting on each other in a way that it could work just with gravity and friction. I’m not sure if that is always possible with straight sticks for general surfaces including negative curvature.
Still, this isn’t necessarily a problem if you are actually connecting the sticks - they can still transfer in-plane and bending forces through the structure - in the little dome we made we used cable ties.