New superbuckyball for math art exhibition of JMM 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.

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.

A postcard from Mr. Horibe

A nice postcard I got from Mr. Horibe:

Angry bird and other 3D bead models

A few 3D models I saw in Ying-Ge, New Taipei City (originally Taipei County) yesterday.

The bead model of angry bird is derived from C₈₀ with some modification for its stomach.