Friday, January 11, 2013
I made a new superbuckyball for the Mathart exhibition of Joint Mathematical Meeting JMM held in San Diego this few days. The original one made by students of TFGS is too big (~60cm wide) to bring to the US. The new one is made by 8mm beads and is about 40cm wide.
Thursday, January 3, 2013
There are only three tetrahedral fullerenes with number of carbon atoms less than that of buckyball. They are C28, C40, and C44, respectively. The spiral code for the smallest tetrahedral fullerene, C28, is [1 2 3 5 7 9 10 11 12 13 14 15]. Following this code, we can easily make its bead model using the standard figure-eight stitch. We can see that, in this molecule, there are 12 pentagons, 3 in a group located at a vertex, and 4 hexagons located on the four faces of the tetrahedron. If we replace these pentagons by heptagons, we get a tetrapod-like structure, in which tri-pentagon vertices become tri-heptagon necks as shown in the following figure.