C60 and T120 with 5mm cateye stones

It's been a while since I made T120 and C60 sometime ago. Also, I have given away all other cateye T120 models made by Chern many years ago. Hopefully, I can show more models with this kind of beads in the future.

Two tiny T120 made by Laura Shea

Laura Shea showed me these two beautiful T120 made of tiny crystal beads in the Bridges conference. They are so small. You can really wear these two carbon nanotori as earrings.

A few bead models of T120s

Here are the bead models of toroidal carbon nanotubes consisting of 120 carbon atoms students made in the second morning of this activity.

Summer camp 2011

I offered a summer camp (繽紛多彩石墨烯─結構與模型, Amazing graphitic structures or here) on creating structures and models of graphitic materials using a number of different techniques for high-school students in Taichung these few days (7/5-7/7).
Three different techniques we used in this mini-workshop are the mathematical beading (one and half days), modular origami based on PHiZZ units (half day) and zometool (half day).

1. 7/5 morning: Students learned the structures of Platonic solids and created bead models of tetrahedron, cube, dodecahedron (C20), and C24. I found that it is very useful to construct these simple trivalent Platonic solids first using beads with rod-like shape. With this, students can become familiar with the basic technique of right-angle weave.
2. The projects for the 7/5 afternoon is to construct bead models of C60 and C80. Most students can finish these projects in three hours.
3. 7/6 morning: Chern spent an hour to explain the molecular structures with jmol (a powerful program for visualizing any kind of molecular structure) first. Particularly, we use C60, T120 and so on as examples. In the next two hours, students started to make bead model of T120. All students succeeded in making their own beaded T120.
4. 7/6 afternoon: We switched to modular origami using PHiZZ units. The only project for this part is to make a dodecahedron.
5. We planned to build a giant concentered multilayer carbon onion consisting of 6 layer of icosahedral fullerenes using the Zometool tomorrow morning (7/7).



Participants:
1. TAs: Chern Chuang, Yuan-Chia Fan and Qian-Rui Huang.
2. twelve students from Taipei (2), Taichung (5), Changhua (4), and Tainan (1)..

Here are a few photos from the camp.






Two T120s that were constructed by students:

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, :-)).

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.

Metalwire stands for bead models

I bought two little metalwire stands for my beadworks from a souvenir store in the Taipei zoo, the largest zoo in Asia according to the Wikipedia.

(T120 made with 180 6mm beads and 0.6 mm nylon thread. I took this photo on the high speed railway back to Chu-Bei.)

Torus C120 with Crystal Beads

Last week Qian-Rui and I went to 延平北路 for the properly sized beads that he needed to construct the beaded EMACS in the previous post. I also bought some beads made of artificial quartz and here is the results:

More toroidal carbon nanotubes (TCNTs)

Here are a few toroidal carbon nanotubes I made a long time ago. There are two types of TCNTs. Smaller TCNTs consist of 120 carbon atoms. So we need 180 beads to construct them.

Larger TCNTs consists of 240 atoms. So a total number of 360 beads are needed to make them.

From New Album 2007/11/6 PM 9:49

C60, C70, C80 and T120

More pictures

Some more pictures I took at 新光三越. I had two beaded models with me that day (Second day of the Chinese new year, 大年初二).

Yet another T120

Constructed by Chuang

sp3 hybridization

The structure shown in the right of following figure has demonstrate that one can, in general, make 3-D structrures that contain the sp3 bonding. Of course, it is harder to weave this type of structures.

From beaded fullerene

Chuang made them.

Another photo for the Cat's eye gemstone

I took this picture with my Lumix.

Cat's eye gemstone T120

Cat's eye gemstones are perfect materials for making high-quality beaded molecules. Although the price for 6mm beads is more expensive that that of plastic beads, it is still within the affordable range. Here are another two T120s made from the 6mm cat's eye gemstones. I guess the raw materials for one T120 cost about US$10 dollars.


constructed by Chuang

碳環120 (TCNT 120)

今天到數學系給個講演，講題為「化學、幾何、藝術：芙類分

子的美妙世界」。

也把這個碳環120送給數學系，作為台大數學月的禮物。

This month is the mathematical month of NTU.
I gave a talk, "Chemisty, geometry, and art: the wonderful of fullerenes", at the department of mathematics of the Taiwan university today. Here is the TCNT 120 I gave math dept as a gift.

T240 Made with Pill-like Beads

T120 weaving code

Here is the weaving procedure I used for creating T120 toroidal nanotube.
This code is resulting from my experience. The details may vary from time to time.



As I have addressed before, I separate the weaving procedure of a torus into two steps: in the first step, we weave the inner part of the torus; and in the second step, we weave the outer part. It is obvious why the inner part has to be built first, otherwise it will become difficult to weave the inner part if we weave from outer part inward.

You may wonder why I didn't follow the latitude completely for T120. The reason is that I want to avoid the the awkward position that may arise if I follow the latitude from inner part. If I weave all ten heptagons at the beginning, later on, I still need to return back the connected region between hexagons and heptagons. Usually, it is quite difficult to do that if I use 4mm beads. For larger beads, it may be ok to weave completely along latitude coordinate.

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.

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