互鎖珠串模型的沸石 A 結構 (2022 Bridges 數學藝術展覽)

2022 Bridges Conference Art Exhibition: Interlocked Bead-Chain Model of Zeolite A Structure by Bih-Yaw Jin

該網頁展示了國立臺灣大學化學系教授 金必耀（Bih-Yaw Jin）在 2022 年 Bridges 數學藝術研討會上的作品。

金教授專注於利用創新的三維編織技術，使用 珠串 構建沸石等納米分子的球體堆積模型，展示了這些結構的複雜性和美感。

展出作品：「互鎖珠串模型的沸石 A 結構」

Interlocked Bead-Chain Model of Zeolite A Structure

• 尺寸：50 × 50 × 50 公分
• 材質：20 毫米木珠
• 製作年份：2019 年

沸石 A（Zeolite A），亦稱為 LTA，可以視為由立方體、截角八面體和截角立方八面體組成的空間填充鑲嵌結構，這也被稱為截角立方體蜂巢結構。

在此作品中，金教授採用新穎的三維編織方法，使用精心選擇的兩種不同長度的珠串構建了包含八個單位晶胞（2x2x2）的沸石 A 結構的球體堆積模型。每條珠串由預應力彈性繩串聯珠子組成。模型中的球形珠子代表氧陰離子，而位於四面體內部的較小陽離子則未在模型中顯示。這些作品展示了數學與藝術的融合，突顯了納米結構的美感與複雜性。

© 2025 珠璣科學 |沸石 A

Bitruncated cubic honeycomb 雙截立方蜂巢(2021 Bridges 數學藝術展覽)

2021 Bridges Conference Art Exhibition: Bead-Chain Woven Sodalite by Bih-Yaw Jin

該網頁展示了國立臺灣大學化學系教授 金必耀（Bih-Yaw Jin）在 2021 年 Bridges 數學藝術研討會上的作品。

金教授專注於利用創新的三維編織技術，使用 珠串 構建沸石等納米分子的球體堆積模型，展示了這些結構的複雜性和美感。

展出作品：「珠串編織方鈉石」

Bead-Chain Woven Sodalite

• 尺寸：30 × 30 × 30 公分
• 材質：2 公分木珠
• 製作年份：2019 年

方鈉石 結構可視為截角八面體的空間填充鑲嵌，亦稱為 雙截立方蜂巢 (bitruncated cubic honeycomb) 或 開爾文結構。 金教授的 珠串雕塑 作品可被視為一種廣義的 張力完整結構，由受壓的硬球組件和受拉的彈性繩組成。 這些作品展示了數學與藝術的融合，突顯了納米結構的美感與複雜性。

© 2025 珠璣科學 |雙截立方蜂巢

八面體奈米金剛石（2020 Bridges 數學藝術展覽）

2020 Bridges Conference Art Exhibition: Octahedral nanodiamond by Bih-Yaw Jin and Chia-Chin Tsoo

該網頁展示了國立臺灣大學化學系教授 金必耀（Bih-Yaw Jin）與 左家靜（Chia-Chin Tsoo）在 2020 年 Bridges 數學藝術研討會上的作品。

他們對奈米結構深感興趣，利用數學串珠的角度編織技術，創建了富勒烯、沸石等納米分子的三維球體堆積模型。這些模型作為分子的宏觀價鍵球體模型，展示了其結構的複雜性。

展出作品：「八面體奈米金剛石」

Octahedral Nanodiamond

• 尺寸：22 × 22 × 22 公分
• 材質：木珠
• 製作年份：2019 年

該作品展示了一個具有八個氫終止（111）表面的 八面體奈米金剛石，這是近似 正八面體（柏拉圖五立體之一）的最簡單物理模型。

此三維編織珠串結構由 C₁₆₅H₁₀₀ 組成，包括多層結構，每層皆由 經（0°）緯（90°）的珠串 構成。 總共使用 50 條適當長度的珠串，基於傳統的 平紋織法，在不同層之間交替編織而成。

這些作品展示了數學與藝術創作的結合，突顯了奈米結構的美感與複雜性。

© 2025 珠璣科學 |八面體奈米金剛石

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)

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.

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.

Four face-sharing pentagonal dodecahedra

E. A. Lord, A. Mackay, and S. Ranganathan described in their book, "New geometries for new materials", a simple cluster consisting of four face-sharing pentagonal dodecahedra arranged in a tetrahedral configuration (pp.48). Here is a bead model of this cluster.

In their book, there are more clathrate structures that one might be able to construct with beads.

Clathrate cluster

I bought some more green rice-shape beads last week and managed to finish this interesting clathrate cluster of 60 dodecahedra in the last weekend. One can still see deformation of many dodecahedra in this clathrate cluster though.

Buckyball made of 60 dodecadedra

I made this structure with beads last weekend. Still unfinished. The finished structure should have 60 dodecahedra arranged like a buckball. One has two ways to interpret this structure:
1. If every dodecahedron represents a carbon atom, we have a standard C₆₀.
2. If we still use beads to represent CC bonds, then we have a giant molecule, C₇₅₀. In this molecule, 450 carbon atoms are sp³ hybridized or tetra-valent and 300 atoms are sp² hybridized or trivalent. But I suspect these sp² hybridized carbon atoms are not energetically favorable, so it is better to have hydrogen atoms connected to these sp2-carbons. Then we get C₇₅₀H₃₀₀!



The bead model of this structure (see here) might be first constructed by Emilie. She asked me to comment about this structure in my blog long time ago (I couldn't find the exact location though).

I decided to make one from beads after I saw the same structure made by a toy designer, Dick Esterle, who actually invented this kind of toys, in the Bridges conference last week.

Planar Tetravalent High-Genus Fullerene

You need to have Java installed to see the above figure.

Chiral cube - the generalized Goldberg polyhedra

Chern Chuang discovered that one can generalize the Goldberg polyhedra to those polyhedra consisting of square grids, instead of triangular or hexagonal grids. Accordingly, the following polyhedron can be classified as the generalized Goldberg vector (3,1); while the cuboctahedron and rombicuboctahedron as shown in the previous posts can be classified as (1,1) and (2,0), respectively.

Cuboctahedron & Rhombicuboctahedron

two more pictures of an sp3 structure

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.