A recent paper entitled "Self-assembly of tetravalent Goldberg polyhedra from 144 small components" (http://www.nature.com/nature/journal/v540/n7634/fig_tab/nature20771_F3.html) (published in Nature by Makoto Fujita et al.) described a kind of self-assembled molecular structures based on the so-called tetrabalent Goldberg polyhedra consisting of square lattice decorated with eight triangles.
Incidentally, Chern Chuang also constructed many bead models of this type while he was still a student at NTU.
Every polyhedron of this kind possesses a unique Goldberg vector.
Chiral cube - the generalized Goldberg polyhedra , in this post, a model of (3,1) Goldberg polyhedron is made.