Two more toroidal carbon nanotubes

I made two more bead models for toroidal carbon nanotubes with 120 and 240 carbon atoms last weekend (Christmas holliday in many countries, but not here in Taiwan, :-)).

Collection of a few Goldberg polyhedra

C720 - Goldberg vector (6,0)

Fused C60 dimer - C120

Chern Chuang made a fused C60 dimer a few years ago. I scaned the model by the scanner as follows,

The neck in this structure is basically the same as the inner part of T120. The two C60s in this model is staggered, so it has D_5d symmetry just like that of ferrocene.

I made another one with two different colors last weekend. I managed to use a single color for both pentagons and heptagons. Comparing these two photos, it looks to me that the structure of this model looks a little bit longer than the one made by Chern. I don't have the original model made by Chern with me now. But I believe this is caused by these two different ways I took the photos.

Goldberg Polyhedron (5,0)

Here is the bead model for the Goldberg polyhedron (5,0) The number of vertices in this model is 20(5²) =500. The number of beads (6mm, faceted) used is 500*3/2=750.

My C168

I have made only one beaded C168, which I gave to Dirk Huylebrouck, a math professor in the department of architecture in Belgium, at the Bridges conference this summer. I took the following photo of this bead model at the Hotel in Pecs, Hungary. I am thinking about making another one, maybe this time with giant beads just like Mr. Horibe has used. Unlike Mr. Horibe, I prefer using different colors for nonhexagons. In this structure, all heptagons are in purple beads. One can easily see that these heptagons are separated by on beads (carbon carbon bonds). In this sense, we can call C168 is the buckyball in the hyperbolic space.


Another two photos that contains more bead models I brought to Bridges conference.



Many of these beadworks are given away as souviners for other attendee. The helically coiled carbon nanotube is given to Laura Shea and the high-genus fullerene is to M. Longuet-Higgins. Toroidal carbon nanotube (T120) with 120 carbon atoms or 180 beads (cat-eye stons) is given away to G. Hart. T120 is made by Chern Chuang. All other small beaded balls are gone too. Many of these small beaded balls are made by Q.-R. Huang. The only three left is the bead models for the P-type triply periodic minimal surface, Shoen's I-WP surface and the trefoil knot, respectively.