T120

This T120 is made by some kind of precious stones (4mm). Chuang made it many months ago. The real model is even more beautiful than this picture due to the shimmering color when light shining on.

T360

C36

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

Graphitic D Surface C168

Chuang created this surface:

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].

『串珠分子模型的美妙世界』已經發表出來了

全文的 pdf 檔請到 化學季刊６６卷第一期 去找！



I wrote this article, entitled "The Wonderful World of Beaded Molecules", for the Journal, Chemistry (Taipei). The article can be found here pdf.

Torus with zigzag pattern inside and armchair pattern outside

Six-fold chiral torus with 4-8 polygons

The general tiling rule worked out by Chuang allows that the underlying graphitic honeycomb lattice is tilted by a suitable angle with respective to the edges in the overall polygonal torus. But these kinds of structures usually contain a lot of carbon atoms. It is tedious to weave them out. Here is one of the simplest structure that has tilted graphitic lattice. The price is that we have to use 4-gons in the outer surface and 8-gons in the inner surface of torus, which is not easy to see in this picture.


created by Chuang.

Two tori with five- and six-fold rotation axes, respectively

The two tori, denoted by T5 and T6, in the following picture have C5 an C6 rotational symmetry axes, respectively. The one with C5 axis has 240 carbon atoms (360 beads used). There are 10 pairs of 5-7gons for T5 and 12 pairs for T6. Roughly speaking, the tubule direction will be changed by 36 (30) degrees for T5 (T6), whenever a 5-7 pair is introduced. But, in the middle of a real weaving process when the two ends of tubule has not been connected, I found that the actual bending angle due to a single 5-7 pair is in between these numbers. This indicates that both kinds of tori have extra bending energies not coming from the 5-7 pairs. Curiously, it seems to me the actual molecular modeling supports this observation.

貓眼石串珠分子模型

Beaded models of fullerenes are aesthetically pleasing artworks themselves.


models created by Chuang.

Framework than contains sp3 bonding

Many people have asked me the possibility of using beads to simulate the sp3 bonding. Indeed, it is possible to create sp3-type bonding in principle, but in practice it is harder than sp2-type chemical bonding. Here is a structure created by Chuang long time ago. I don't even remember whether I have posted it or not.

More 3-D tori created by Append Huang: repost from byjingroup blog

Here is a simple example of series of leapfrog transformation. Note that after each operation the number of atoms is tripled.

T120






T360






T1080

Guess What?

Thanks to the great help from Append Huang!

Other high-genus fullerenes need to be worked out

The next genus-3 fullerene

Genus-3 fullerene

Here is a genus-3 fullerene discovered and weaved by Chuang. We thank Prof. Wen-Ching Li (李文卿教授, math dept, Penn State university) for sharing her work on Ramanujan Cayley graphs.


Given away to Prof. Li as a souvenir.

Fused C60 dimer

Scanned pictures (Diane Fitzgerald)

Three amazing beaded structures created by Diane Fitzgerald. Scanned from "The art of beaded beads".

Tetrahedron



Cube



Tetrahedron


＜這些圖可能有版權問題，請勿轉載。＞

The Art of Beaded Beads: Exploring Design, Color & Technique

My wife borrowed this wonderful book from NCTU's library. There are many amazing beadworks by different artists.