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.

A few more pictures from Horibe

I found a few more pictures about Mr. Horibe's (堀部和経) beadworks and workshops in Japan.


He seems to be fond of making beaded structures similar to that of C168 with endcaps.

More pictures can be found here.

Poster for the annual meeting of Taiwan's chemical society

Here is a poster I made for the annual meeting of Chinese chemical society located at Taiwan one week ago. This poster summarizes most of what we have done in the last few years.


High-resolution poster is here.

Mr. Kazunori Horibe's wonderful site

I was informed today by Prof. Sonoda about a Japanese site which contains many interesting beaded fullerenes just like we did in this blog. This site (http://www.u-gakugei.ac.jp/~onodakk/math/beadsindex.htm) is created by a Japanese highschool mathematic teacher, Mr. Kazunori Horibe (堀部和経). In addition to the standard cage-like fullerenes (C60 and C80), kind of toroidal carbon nanotubes similar to our T120, Mr. Kazunori Horibe has also created a number of fullerenes consisted of fused C60.



(Carbon poti donut （波提甜甜圈）. I thought about making this kind of structure before, but didn't really try to do it.)


Incidentally, Chern has created a fused C60 dimer a few years ago, see here. But we didn't pursue further along this direction.

In this site http://horibe.jp/Gr2F.HTM, I also found this picture dated 1/1/2001:

(The giant structure in this picture is essentially a few unit cells of C168 with endcaps, I wish I can play with this kind of giant beads someday.)

We can also see here many more extended structures exactly the same or similar to we have created in the last few years.

Apparently, Mr. Kazunori Horibe has played systematically with mathematical beading for fullerene structures much earlier than we did. Please check his site to see the beautiful fullerene structures he has created. Unfortunately, this site is in Japanese, this may be why I didn't find it through google in the last few years.

There seem to be a commercial site by Mr. Kazunori Horibe too:
http://www.ballstructure.com/ballstructure/.
and detailed instruction on the construction of beaded C60:
http://www.ballstructure.com/ballstructure/KA-AmakingB.htm.

C540

I made another giant fullerene with Goldberg vector (3,3) last week.


Goldberg vector (3,3) gives the position where to put the next pentagon. With this in mind, one can create easily any fullerene specified by the Goldberg vector (i,j).