Posters on beaded molecules

I made a few hardcopy of "beaded molecules" posters (A4 size). They look great!

You can download the high-resolution pdf file of this poster here! (高解析度海報的pdf檔下載)

A new poster - The Fabulous World of Beaded Molecules: Architectural Beauty of Zeolites (串珠分子模型的異想世界：沸石構築藝術之美)

Chia-Chin and I prepared a new poster, The Fabulous World of Beaded Molecules: Architectural Beauty of Zeolites (串珠分子模型的異想世界：沸石構築藝術之美), for a project we did together for the Ministry of Science and Technology (科技部).

You can download the high-resolution pdf file of this poster here! (高解析度海報的pdf檔下載)

Workshop for students from Kanagawa University

I gave one more workshop for students from Kanagawa university, Japan. Today, I tried something new, instead of working on C₆₀ for each student, I asked them work on two zeolite structures, zeolite A and Faujasite, together after making the famous 30-ball Sangaku problem, which just gave them enough beading experience to move on. Both of these two zeolite structures consist of the same structural unit (Secondary Building Units, SBUs), namely truncated octahedrons. It seems to be easy for them to work together, then combine them into these two framework types. Here are a few pictures from the workshop.

Students were very happy when they succeeded in making the zeolite A.

科學遇見藝術─串珠分子模型的異想世界

Chia-Chin and I recently wrote a short overview manuscript entitled "Where Science Meets Art - The Fabulous World of Beaded Molecules" about beaded molecules for a meeting which will be held in Shandong, China this weekend.

Note: 由於這篇文章太晚寄出，最後未出現在論文集中。(Sept. 7, 2007) 我會另尋適當的雜誌發表。

Two articles about the construction of gyroid- and diamond-type triply periodic minimal surfaces

I wrote two articles in Chinese for the Journal, Chemistry Education in Taiwan (臺灣化學教育) last year. The pdf files have just come out:
1. 左家靜, 莊宸, 金必耀, 大家一起做多孔螺旋與鑽石型三度週期最小曲面的串珠模型（上）─立體幾何介紹，2014 臺灣化學教育, 328-335.
2. 莊宸, 左家靜, 金必耀, 大家一起做多孔螺旋與鑽石型三度週期最小曲面的串珠模型（下）─實作，2014 臺灣化學教育, 336-344.
The title can be translated as "Application of mathematical beading to carbon nanomaterials - A hands-on, collaborative approach to gyroid- and diamond-type triply periodic minimal surfaces with beads, I and II", literally. I described a simple modular approach which was developed mainly by Chern Chuang for making gyroid- and diamond-type Triply Periodic Minimal Surfaces.

Eight convex deltahedrons

I made all convex deltahedrons with tubular beads early this year. There are infinite deltahedrons, but only eight of them are convex.

(Photo by B.Y. Jin, Mar. 15, 2015)

Bead models of four Archimedean solids

Truncated octahedron, truncated icosahedron (C₆₀), truncated cuboctahedron (great rhombidodecahedron), truncated icosidodecahedron (great rhombicosidodecahedron):

Two pictures from Gabala, Azerbaijan

I took a few pictures of bead models I brought to Azerbaijan.
The first one is a model of EMACs (extended metal atom chain) with 9 metal ions. This model was made by Qian-Rui Huang many years ago.

The second one is a model of zeolite which I gave to Prof. Yin-Xia Wang of Beijing Univeristy as a gift. She is an exert on zeolites.

A few pictures from the IChO 2015

(in Aliyev Cultural Center, Baku, Azerbaijan)

C60's bead models for the International Chemistry Olympiad 2015, Azerbaijan

I am a member of Taiwan Chemistry Olympiad team for the 2015 IChO (International Chemistry Olympiad) which will be held next week at Baku, Azerbaijan. We prepared many C60 bead models as souvenirs for participants from around the world. To make about 200 bead models of C60. we got help from chemistry teachers and many senior students of the Taipei First-Girl School (TFGH). Most of these students have just got acceptances from colleges and have some spare time to help us prepare these beautiful bead models.

However, it is fun to make one's own beaded C60, so Chia-Chin and I also prepared about 200 kits of materials and detailed instruction for making C60.

A few photos from the NTU Chemistry Camp

I gave a workshop for the summer chemistry camp of the chemistry department at the National Taiwan University early this month. This is a summer camp for the local high school students. There are about 60 participants this year. Here a few photos from the workshop:

The title and the first slide of my workshop for the chemistry summer camp:

Molecular rugby ball vs molecular baseball

I noticed that the last two of C36's fifteen isomers, namely C36:14 (point group, D2d) and C36:15 (D6h), are very similar to a baseball and a rugby ball, respectively. Also, a Stone-Wales transformation can bring one of them to the other.

Workshop at Bar-Ilan University

Tel Aviv, Israel (以色列特拉維夫)，2014/11/18

Workshop for visitors from Waseda university

(日本早稲田大學師生, 2015/5/7)

Bead model of a Trinoid

Tsai-Rong Liu (劉采容), an undergraduate at chemistry department of the National Taiwan University, built this interesting graphitic structure which approximates the trinoid, a minimal surface with three catenoid openings. Similar graphitic surfaces with k catenoid openings, i.e. k-noids, can be built similarly.

作品完成時間（約）：2015/4/15
作者：劉采容

Hyperbolic buckyball

拍攝時間：2015/4/28; 地點：北一女
作品完成時間：2015/2/8

Torus knot (1,2)

Kazunori showed me this beautiful torus knot (1,2) he made a few days ago. This structure can be classified as a torus knot, or more specifically a twisted torus without knot at all. The space curve that this tubular structure approximates can be described by the parametric equations for the torus knot (q=1, p=2). Therefore, it is reasonable to call it as the torus knot (1,2).

To me, this structure seems to be a perfect example to show the influence of the particular operation, Vertical Shift, described in the following papers:
1. Chuang, C.; Jin, B.-Y. Torus knots with polygonal faces, Proceedings of Bridges: Mathematical Connections in Art, Music, and Science 2014, 59-64. pdf
2. Chuang, C.; Fan, Y.-C.; Jin, B.-Y. Comments on Structural Types of Toroidal Carbon Nanotubes, J. Chin. Chem. Soc. 2013, 60, 949-954.
3. Chuang, C.; Fan, Y.-C.; Jin, B.-Y. On the structural rules of helically coiled carbon nanotubes, J. Mol. Struct. 2012 1008, 1-7.
Another related operation is the Horizontal shift, which is not used in this structure. Applying these two operations carefully (usually nontrivial), one can mimic the bending and twisting of many space curves in an approximate way.

作品完成時間（約）：2015/4
作者：堀部和経

Interpenetrated Boerdijk–Coxeter helix

Inspired by the work of Rinus Roelofs.
作品完成時間：2015/4

Circular helix winding around a central torus

Horibe-San just constructed another beautiful beadwork, a circular helical carbon nanotube (or circular carbon spring) winding around a toroidal carbon nanotube.

作品完成時間（約）：2015/4
作者：堀部和経

Another surface with negative Gaussian curvature

2015/4/4

Bead model of the Chen-Gackstatter surface of genus 1

I made a bead model which approximates the minimal surface, Chen-Gackstatter surface of genus 1, for the spring break.

Other Chen–Gackstatter surfaces can be made with mathematical beading, in principle!
2015/4/3

Torus knot (2,9) by Kazunori Horibe

Kazunori email these photos of a beautiful bead model of (2,9)-Carbon nanotube torus knot (CNTTK) he just made the other day. To make the structure more clearly, I also use the Grapher to create the corresponding torus knot.

Hyperbolic soccerball

I posted many hyperbolic bead models before. But most of them are periodic surface structures in 1- to 3-D dimensional spaces. Examples are various periodic minimal surfaces. In these models, one needs to pay attention to the subtle periodic conditions in the course of beading. Sometimes, it makes the beading quite difficult.
Here, I show a simple construction of hyperbolic soccerball (truncated order-7 triangular tiling) consisting of infinitely many heptagons (blue beads), each of them are connected to seven neighboring heptagons by only one carbon-carbon bond, which is represented by a yellow bead in the model shown below.

Following the spiral beading path by adding hexagons and heptagons, eventually one obtains the hyperbolic soccerball, or more exactly a hyperbolic graphitic snowflake. There is no need to worry about the periodic conditions among different parts of the structure.

From wiki: Truncated order-7 triangular tiling

In principle, one can also use kirigami (paper cutting) to make a model of the hyperbolic soccerball. But I found that the beading technique is much easier for making robust structure of this object due to the nature of mathematical beading. Also the bead hyperbolic soccerball should be able to model the local force field of hyperbolic soccerball to certain extent because the bead model not just gives the connectivity of the molecular graph right, but also mimics the microscopic repulsions among chemical bonds.