Molecular rugby ball vs molecular baseball

I noticed that the last two of C36's fifteen isomers, namely C36:14 (point group, D2d) and C36:15 (D6h), are very similar to a baseball and a rugby ball, respectively. Also, a Stone-Wales transformation can bring one of them to the other.

Tetrahedral C28 and related structures

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.

Using these tetrapods as building blocks, we can get the following diamond-like structure. In fact, this is exactly the structure Mr. Horibe put in the postcard. OK, if we start from other tetrahedral fullerenes such as C₄₀ and C₄₄, we can find out a lot more diamond-like structures.

More pictures

C26

Spiral (weaving) code: 1 2 3 5 6 7 9 10 11 13 14

C60 Isomer with D3 symmetry

Michel Deza, Ecole Normale Superieure, Paris; Mathieu Dutour, Rudjer Boskovic Institute, Zagreb

Fullerene 528 (Td)

Spiral code: 123579 10 11 12 13 14 15

C36

spiral code: [234567 14 15 16 17 18 19] 5¹²6⁸

C20 and C24

I made these two simplest fullerenes: C20 and C24. C20 was made in Prof. Chiu's group meeting yesterday afternoon. These two fullerenes are quite easy to make for experienced beaders, but not necessary easy for beginners. We have about 15 students in this mini-workshop, most of them have no experience on beading. My goal is to introduce the world of beaded fullerenes to these people with one hour lecture and then let them have a hands-on experience by making the simplest C20. C20 is a dodecahedron with all carbon atoms located on the vertices. Even though, you can create this molecule by simply weaving 12 pentagons. But there are many subtle points in the whole weaving process, because the number of beads and number of holes that have to be added and passed varies from time to time. They are not easy to explain before students start to bead. I will think about how to explain these subtly points later.




The spiral codes are [123456789 10 11 12] and [23456789 10 12 13], respectively. Or put another way, [555555555555] and [65555555555556].