T240 Made with Pill-like Beads

C80 again!

Helical nanotube

Two-layer tetrarhedron

High-genus fullerene: two-layer dodecahedron

D168

P surface

C60 with cylindrical beads

Here is the C60 made from the cylindrical beads. The advantage of using this kind of beads is that the beaded representation is indeed the pi-bond network as we have emphasized repeatedly before. Pedagogically, this is very important for students to understand. Compared with spherical beads, this kind of beads may be better for beginning students since it is closer to chemical bonds introduced in the textbook.

The capsule-shaped beads are not perfect either. The most important disadvantage is the structural stability of physical models created from this kind of beads is not as stable as the same structure made from spherical beads. It is quite easy to distort the shape of this kind of model. The other advantage is that much longer fishing thread is needed to make a model. This makes the construction a little bit harder, particularly for larger systems.

Beaded D168

Here is the first beaded model of D168. D168 has diamond structure. So it is an extended structure. Here I only made part of the whole structure based on the admantane. We can actually infer from the factorization of 168=7*24=7*12*2=7*3*4*2 many important structural information.

Based on the fact that every heptagon in D168 is connected to seven other heptagons by a 6-6 bonds, and the local structure is a tetrepod, so these two numbers correspond to 7*4 in the factorization. The remaining two number are 3 and 2. Inspecting this structure, we know 3 corresponds to the three heptagons surrounding the neck and 2 is the two tetrapods in a unit cell. Each tetrapod has 84=7*12 carbon atoms.

Platonic solids with cylindrical bonds

Cylindrical beads that have capsule shape are perfect pedagogical materials for creating physical models of fullerenes since they can look like the chemists' intuition of chemical bonds and, at the same time, effectively mimic the steric repulsion among different beads. To demonstrate these points, here, we use these beads to create the five Platonic solids. 

Chemical bonds as cylindrical beads

I found this kind of cylindrical beads in one of local stores (廣昕) last weekend. They look perfect for mimicking chemical bonds. I will try other structures out later this month. 

HG-dodecahedron: one more patch to go

HG-dodecahedron in progress

Caged Ping-Pong Ball

Endcapped Helix

A beaded fullerene in hand is worth two in computers.

High-genus fullerenes belonging to icosahedral group are beautiful molecules. We can expect their beaded models should be even more aesthetically pleasing. The only problem is that they are hard to make, not only because so many beads are needed even for very simple systems, but also because the algorithmic rules to generate them are quite complicated. Here we finally have the first beaded two-layer dodecahedron with twelve connected holes in its preliminary stage designed and cteated by Chern Chuang. Since this preliminary structure is already quite amazing, so I scan it and posted it here. 


Amusingly, this structure reminds me of Darth Vader in Star Wars. How do you think?

Schwartz D-Surface: a preliminary try

I have tried to make a beaded model for the Schwartz D-surface several times, but all failed. Finally, I seem to find out the correct rule for this structure. Here is the very preliminary result. Since the current structure is quite flexible, so I may need to redo it completely.

Eventually, I would like to have structure like this:

Beaded model for D168!

Finally, I have made a beaded model for the famous D168 fullerene, which is essentially corresponding to the C60 in the hyperbolic space.

D168

The 3D structure of D168 we posted a few days ago is incorrect. Chuang has now the correct structure shown below:











I thought it is not a bad idea to have a beaded model for this structure. Now I am still at a very preliminary stage (see the picture shown below).


Eventually, I expect to have a D168 structure similar to Adamantane:

C80

The spiral code of C80:

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.

C60 Isomer with D3 symmetry

Michel Deza, Ecole Normale Superieure, Paris; Mathieu Dutour, Rudjer Boskovic Institute, Zagreb

F96

Michel Deza, Ecole Normale Superieure, Paris; Mathieu Dutour, Rudjer Boskovic Institute, Zagreb

Fullerene 528 (Td)

Spiral code: 123579 10 11 12 13 14 15