I found an interesting site:
Straw polyhedron and other nets
This page discusses the application of straws to the construction of polyhedron. Here are some of the poyhedron they built:
Straw polyhedrons or straw fullerenes (restricted to trivalent structures) are formally the same as the beaded fullerenes we advocate in this blog. But there is a major difference, the straw models do not simulate the correct sp2 force field of fullerenes, while our beaded models do. Thus it is hard to create large and complicated fullerene structures with straws and string. On the other hand, based on our previous experience, the beaded models can effectively simulate arbitrary fullerenes which may be large and complicated as shown in many pictures posted in this blog.