Saturday, December 11, 2010

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.

3 comments:

Chuang Chern said...

謹賀新世紀!!

Bih-Yaw Jin said...

I didn't understand correctly about these structures by Mr. Horibe. His models are quite different from structures Chern and I made. Basically, he used C60 as starting point for creating other complicated structures which include the giant structure shown in the picture. It has no relation to C168 as I incorrectly made the connection. C168 is the buckyball in the hyperbolic space in the sense that every heptagon is separated by other neighbored heptagons by only one CC bond. The structures created by Mr. Horibe do not have this property though.

The basic idea of Mr. Horibe is to fuse two C60 along 5-fold axis. One can do this operation along any of 12 5-fold axes. Then one can build quite a number of different structures such as tetrahedron and dodecahedron using the C60 as vertices. I will talk more about this later.

Bih-Yaw Jin said...

In addition to icosahedral C60 as building blocks, another one is tetrahedral C84. More often, Mr. Horibe used C84 to make different kinds of giant graphitic structures.