Please have a look at
the object in question is a truncated icosahedon whose sides are pearls.
It is an interesting little bauble which can be found in some cheap jewelry stores.
Each pearl is drilled and through the hole thus created there are two threads.
Upon exiting the hole (therefore at a vertex) the threads are directed towards adjacent pearls.
Since at each vertex three sides (pearls) come together, there are three threads at at each vertex (these threads are visible if one looks at the picture carefully).
Any idea how this "threaded" truncated icosahedron was put together?
I suspect this may have to do with graph theory, an assumption very easy to make since I know absolutely nothing about the subject.
My ultimate goal is to be able to put together such a polyhedron using small pieces of pipes and string, and who knows may be other polyhedras.
I have built a truncated icosahedron with Zometool parts but I have not been able to find a solution, only conjectures.