Modelling a freeform magnetic mesh

hi all. im new to blender so bear with me please. im an architect and sculptor and at the moment design with a magnetic toy set called supermag. its steel balls and magnetic rods in length 1 and 1.414, the diagonal of one.

now, if im building a model that only consist of a load bearing outside shell or mesh the actual shape is a result of a balance of forces around the nodes. since the rods can freely rotate around the balls all angles change if i exchange one rod. all i know about my sculptures is the rod lengths and the node connections.

the question is how to model this in blender?

if i had a solid point to start with it could be done by somehow constructing all other node points through triangulation or the intersection of three mathematical spheres whose radius are the rod lengths. but i cant find that function in blender.

here is a simple woodpecker shell model, completely hollow. how would you go about modelling that in blender?

this is my signature shape which is based on half a cubeoctahedron. thats much easier because it starts with a hexagon and has 3 tetraeder inside.

here it is in magnets:

here is a video that describes bones and rigging which could be the solution but seems to be overkill.