Prof. JT. Chen forwarded me a message from Sharon, an audience of my talk early this month. Sharon has a simple mnemonic by her son for making the beaded C60. In C60, every pentagon is surrounded by 5 hexagons, and every hexagon is surrounded alternatively by 3 pentagons and 3 hexagons. (五邊形的周圍是六邊形,六邊形的周圍是一個五邊形接一個六邊形.) One can easily create a beaded C60 by following this simple rule.
Two beaded models made by Sharon:
Indeed, one does not need spiral code to make C60. But to make an arbitrary cage-like fullerene (genus=0), spiral code is the only information we need. The shape of resulting beaded structure is always similar to the shape of the corresponding microscopic fullerene. It is quite amazing that one can create the faithful structure for an arbitrary fullerene with beads so easily. A simple explanation is that hard sphere repulsion among beads effectively mimic the valence-shell electron-pair repulsion of trivalent carbon atoms in fullerene molecules.
Additionally, if one want to make a beaded C60 with two different colors, a single color for pentagons and two different colors alternatively for hexagons. Then one doesn't need to use the mnemonic as given above. One can just pay attention to the colors only. Starting with a pentagon with a single color, then hexagons with two colors alternatively, eventually, one should get a beaded C60 correctly.
A few beaded C60s (10mm faceted beads) I made in last week:
See also a discussion in the previous post.