Tensegrity- Joining Rigid Bodies with Strings

Hi, I’ve been using Blender for about a year now… but one of the things I still can’t figure out is how to anchor a vertex of one object to the vertex of another object… with physics enabled for both objects. I know a little about parenting and armatures, but I can’t find a way to do this for the life of me.

For example, I would like to make a structure like this:

The elastic strings are connected to the solid rods, and when proportioned and positioned correctly, they make a free-standing structure. I want to enable rigid body physics to the rods and (I assume) cloth physics to the strings. My question is how do I attach the end of a string to the top of the rod (as if they are glued together at that point) and then run the physics simulation?

Hope this makes sense, and thanks in advance for any help you can give me!

I’ve set it up with vertex parenting, but I can’t figure out how to make multiple parents have multiple children. Also, the strings end up going through the floor (which is a plane with passive rigid body applied).