T240 & C140

The aspect ratio of T240 (12mm) in previous post seems to be too large. My scanner probably has some problem to generate correct aspect ratio for large objects. So I just manually adjust it with the Illustrator.

一種碳環，兩種大小

T240 with 12mm and 4mm beads respectively.

The Three Canonical TPMS and Their Graphenoid Representations

tensegrity structures and straw

Straws can also be used to construct tensegrity structures:
Soda Straw Tensegrity Structures:



My 18" 270-Strut Tensegrity Sphere

Creative Science uses straws and suitable trivalent connector to build C60.


Nice instruction on straw icosahedron( A japanese site ) More can be found at this site.

Straw polyhedron

I found an interesting site:
Straw polyhedron and other nets


This page discusses the application of straws to the construction of polyhedron. Here are some of the poyhedron they built:

Tetrahedron


Octahedron


Icosahedron


Straw polyhedrons or straw fullerenes (restricted to trivalent structures) are formally the same as the beaded fullerenes we advocate in this blog. But there is a major difference, the straw models do not simulate the correct sp2 force field of fullerenes, while our beaded models do. Thus it is hard to create large and complicated fullerene structures with straws and string. On the other hand, based on our previous experience, the beaded models can effectively simulate arbitrary fullerenes which may be large and complicated as shown in many pictures posted in this blog.

almost 2x2x4 P surface

One more unit cell to complete a 2x2x2 P-Type TPMS model

1x2x2 P-Type surface

Finally, I have a P-Type sufrace (made with 6mm faceted beads) with four unit cell. I made a serious mistake in the weaving of the fourth unit cell. It took me another day to have this beautiful beaded model.

New Light Tent

I uploaded some photos I took. This time I removed the translucent papers off the tent.

Please take a look of my picasa album.

The photos beyond this one are took in the new light tent while the ones before it are not. I doubt that my photos are yellowish is because my cam is actually reaching its lifetime.

Real Schwarzite D-Surface Graphenoid

Later last night I finished the coding of the "real" Schwarzite D-Surface Graphenoid generation, which is done by finding the dual lattice of the following infinitely extending deltahedron:



Which is copied from Ken Brakke's site, who is the author of Surface Evolver. And his TPMS gallery always gives me a great deal of help when doing the coding of negative-curved graphenoid.

The dual of this deltahedron is then the Schwarzite D-surface graphenoid with minimal number of atoms per unit cell. (There are 8 unit cells in the figure!)



A view from high symmetric point:



Here I also present some figs of the second smaller one:






One with four unit cells:

P-type surface

T120 with shell beads

Chuang's work again.

rhombicuboctahedron

great rhombicuboctahedron

cuboctahedron

octahedron

truncated octahedron

Cube

C20, Dodecahedron: another beaded representation

truncated tetrahedron

Tetrahedron

capsule shaped beads

The new type of beaded fullerenes designed by Chuang strongly suggests that very good 3D structures of fullerenes can be constructed from capsule shaped beads.



On one hand, this kind of beads is similar to shape of a chemical bond that most chemists are familiar with; on the other hand, the steric hindrance among different beads can still effectively mimic the sp2 repulsion.



Unfortunately, capsule shaped beads are not popular in beading society. We couldn't find this kind of beads commercially available locally.

C60 with each bond built from two spherical beads and one tube

In the following figure we show the beaded model for C60 based on the composite bead technique. The final shape is not quite satisfying as we can see it is a little bit distorted. This is probably due to that the sizes and shapes of the constituent beads and tubes are not exactly the same. I believe a better structure can be constructed if we can control the sizes and shapes in a better way.

Two more beaded C20s

I just made two more dodecahedral C20 in order to make my point clearer. The model in the left of the following figure is made from the standard spherical beads. Due to the hard-sphere repulsions among nearest beads, the resulting structure is quite stable even under moderate external pressure.

To some people, particularly some organic chemists, the most confusing part of our beaded representation of fullerenes is that the beads in the model stand for bonds instead of atoms as commonly used in stick-and-ball models. Thus we need thirty beads to make a C20. Since most people are used to the concept that any spherical object in a molecular model must correspond to an atom, thus our beaded models based on spherical beads may cause some confusion. The simplest way to solve this problem is that we should use beads with large aspect ratio to build our physical models. The model in the right of the following figure is constructed with this kind of beads. The beads as chemical bonds can be seen clearly. Unfortunately, this kind of beads cannot mimic repulsions among sp2 orbitals as good as spherical beads.

An effective strategy to improve this problem is based on the type of beading introduced in previous message.

Dodecahedral C20 with correct bond shape and force field

Previously, I have shown that beads with spherical shape can effectively mimic sp2 force field of fullerenes. However, these beads represent bonds instead of atoms. This may lead to confusion for students. We can avoid this problem by using beads with large aspect ratio, but the resulting structure usually has poor mechanical stability. Here Chuang has created a nice beaded fullerene of C20 (Ih) which can clearly exhibit the bond network of fullerene and at the same time possess great stability.