## Friday, October 7, 2011

I took a few photos for making bead model of C60. This will be helpful for learning the so-called figure-eight stitch (or right-angle weave) and the beading rule of C60 I mentioned before.

South hemisphere:

North hemisphere:

* General instruction:
1. There are 32 polygons consisting of 12 pentagons and 20 hexagons in a C60.
2. Every pentagon is separated from neighbored pentagons by eactly one CC bond.
3. If we choose one color of beads for pentagons and the other for the rest, one would find hexagons made of two colors alternatively.
4. It is better to view C60 as a sphere consisting of six layers of polygonal strips. For the south semisphere, they are basically a pentagon for the south pole, five hexagons next, 10 polygons consisting of 5 pentagons and 5 hexagons. Reverse the beading sequence, one gets the north semisphere. (This is what people called the spiral code.)
Of course, one should always check the sequence of colors of beads one is going to bead and make sure that they satisfy the color coding mentioned in 3.
For beginners, this is usually the hardest part and mistakes occur easily. Most often, wrong number of beads are added or some beads are not threading through first. But, if one can pay attention to the number of beads in the next group one is going to make, it should be trivial to figure out how many beads are already there and how many more one should add.
If two colors of beads are used, one can simply pay attention to color. Beading process for a C60 becomes trivial.

The beading procedure can be summarized by the spiral code on the following Schlegel diagram of C60. For C60, it is [1 7 9 11 13 15 18 20 22 24 26 32], which is essentially the positions of pentagons along the spiral path starting from south pole to the north pole. It is not hard to find this code is the only information we need to create a bead model of C60. Similarly, one can create any other cage-like fullerene by its spiral code only if the fullerene possesses it.

A list of fullerenes up to 100 carbon atoms is given in the appendix of the book "An Atlas of Fullerenes" by P. W. Fowler and D. E. Manolopoulos. So one can create any fullerene easily by following its spiral code. The shape of the resulting bead model is basically consistent with the corresponding fullerene.