"Threaded" Truncated Icosahedon Please have a look at 
http://www.cijoint.fr/cjlink.php?file=cj201006/cijHr27640.jpg 
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.
Thank you.
 A: The points of the icosahedron are known. Coordinates can be found for each point. From these the coordinates for the truncated icosahedron can be derived. From these the points on the edges where the pearls can be placed can be derived. The resulting polyhedron depends on the properties
of the points placed on the edges. Is there a single point bisecting the edge. Are there two points
symmetrically placed about the midpoint of the edge? If so how. Once this choice is made the resulting points coordinates can be determined and from this the lengths of the sides which ought to give enough information for construction.
In regards to the question about the easiest way to build a truncated icosahedron in the comments. I would use the fact that all if its faces are equilateral hexagons and pentagons with two pentagons and one hexagon at each vertex. If I could get rigid hexagons and pentagons I could fit them together and I would be able to get the polyhedron relatively easily. It is much easier to construct this because all the faces are regular polygons so they could be constructed first and the rest of the construction is relatively easy.
