Slides for making a beaded C60

I would like to thank Rochelle for pointing out that the procedure in the tabular form I posted before is incorrect. I have to admit that I have never used this kind of table for making C60. I think it is easy to make mistakes by just following this table literally and without thinking. If you are a little bit careful, you should be able to see the hidden rules for making the C60 just after about 10 steps.

Below is a few slides I used to teach people how to make a buckyball.


But, it is much easier to follow the simple mnemonic for making a buckyball.


If one wants to make a beaded C₆₀ with two different colors, a single color for pentagons and two different colors alternatively for hexagons, one can use these two colors as a mnemonic for deciding whether one need to make a pentagon or hexagon in the next step. Remember that in a C₆₀ every pentagon is surrounded by 5 hexagons and every hexagon is surrounded by 3 pentagons and 3 hexagons alternatively. Then one can start with a pentagon with a single color, then hexagons with two colors alternatively, eventually, one should get a beaded C₆₀ correctly without using any other information.

A nice mnemonic for making beaded C60s

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.

Workshop at Taichung

I gave a one-day workshop on the beaded molecules for some junior high school students this summer (7/2-7/3/2009) at Taichung, Taiwan. Here is a picture about the workshop.



In the morning, after a brief introduction on the chemical bonding and a few simple molecular structures, I then started to teach student the platonic solids and basic weaving techniques by asking them to make a C20 (a dodecahedron). I simply asked students follow my instructions step by step without too much explanation. This is because, I think, it is important to have some hands on experience for constructing beaded fullerenes first. Some students can get the basic rules of weaving just after a few steps, others may take a longer time and kept asking me how to do the next step. But it took about an hour for all students to get the first project done. I also found that it is better to use larger beads around 10mm to 12 mm for students who have no experience in beading. To create a C20, one need 30 beads. So it is not too expensive even for a group of 50 students.

The next project in the afternoon was to construct a C60. Of course, before we started to do that, I explain the icosahedron, truncated icosahedron and a few background information on fullerenes to them. Unlike C20, where all atoms and bonds are equivalent, here we have two different bond types, 5-6 and 6-6 bonds, so it is natural to use two different color of beads for the construction. In fact, this is not a burden for weaving. Instead, color of beads can be used as a mnemonic aid for denoting the place of pentagons. One needs 90 beads to represent chemical bonds in a C60. Since students have some experience in the morning for making a C20, I find it convenient and more cost effective to use 6mm beads with two different colors for students to work on in this project. It took about 2 hours for most of students to construct his or her C60.


The picture shown below is the C60 I made in this workshop. At the end, I gave it to one of students in this workshop as a souvenir.