2021 數感嘉年華 之 挑戰珠立方

Bead-Chain Building Blocks

Contained within the box is a bead chain cube, showcasing an innovative method for building tensile structures. This wooden model utilizes four pre-tensioned linear bead chains interconnected with suitable cross-links. The elastic properties of the bead strings generate tension, causing the beads to repel each other when tightened. This interaction between string tension and bead repulsion ensures the overall self-balancing of the structure.

Bead-Chain Cube (BC-Cube):

Take apart BC-Cube to obtain four chains of five beads each.

Challenge 1: BC-Cube

The first task is to reconstruct the four five-bead chains into a cube structure as depicted in the diagram below. The eight terminal beads of these chains align with the vertices of the cube, while the remaining twelve beads are distributed along the cube's edges.

Challenge 2: Giant Tetrahedron

The next task is to link the same four five-bead chains into a tetrahedral arrangement as shown in the diagram below. Each edge of the tetrahedron consists of four beads, and each triangular face contains a total of ten beads.

Basic Operation

The fundamental process in constructing a bead chain model involves "cross-linking". As illustrated in the figure below with two chains of four beads each, the method entails stretching and crossing these chains over the gap between beads. The pre-stressed elastic strings create tension, causing the beads to snugly tighten and wrap around the crossing point.

Bead-Chain Molecular Models

Bead-chain building blocks enable the construction of valence sphere models for various molecules. In these models, beads symbolize the valence electron pairs of the molecule, while the taut elastic strings provide the necessary attractive force to bind these electron pairs together within the molecule. By carefully balancing tension and compression, bead-chain building blocks effectively simulate the equilibrium structure of numerous molecules.

Cubane, with the chemical formula C₈H₈, features carbon atoms located at the eight vertices of a cube. These carbon atoms are bonded together by twelve carbon-carbon bonds, with the carbon-hydrogen bonds oriented outward from the structure.

See Also

• Chinese(中文)：珠串組合益智積木與珠立方
• Chinese(中文)：2021 數感嘉年華 之 挑戰珠立方 poster

External links

• 2019 Bridges Conference Art Exhibition: BC-Cube and BC-Dodecahedron by Bih-Yaw Jin
• Bih-Yaw Jin, Bead-Chain Construction Set and Interlocking Puzzle Inspired by Polyhedranes, Proceedings of Bridges 2019: Mathematics, Art, Music, Architecture, Education, Culture, 553–556.
• 2024 Bridges Conference Art Exhibition: Polyhedrane with Great Rhombicuboctahedron Skeleton and Bead-Chain Buckyball by Bih-Yaw Jin
• 2020 Bridges Conference Art Exhibition: Octahedral nanodiamond by Bih-Yaw Jin and Chia-Chin Tsoo
• 2021 Bridges Conference Art Exhibition: Bead-Chain Woven Sodalite by Bih-Yaw Jin
• 2022 Bridges Conference Art Exhibition: Interlocked Bead-Chain Model of Zeolite A Structure by Bih-Yaw Jin
• Facebook: 珠璣幾何 GeoBeading

珠串組合益智積木與珠立方

珠串積木是一種全新的張力構建體系，利用具有預應力的線型珠串，通過適當的交叉連結，可以用來搭建各種張力結構。線型珠串中繃緊的彈性繩，具備有預應力因而產生張拉力，並造成珠子彼此間硬殼排斥力與壓縮力，張拉力與壓縮力的均衡，讓整體結構達到自平衡的狀態。這種珠串積木可以應用來建構許多微觀分子的價球模型，其中珠子代表分子中的價電子對，而繃緊的彈性繩給出張拉力，扮演將電子對束縛在分子內所需的吸引力，通過張拉力與壓縮力彼此的均衡，巧妙地模擬微觀分子的平衡幾何結構!

最簡單的珠串積木系統由四條五珠串組成，可用來建構幾個最基本的多面體烷——四面體烷、三棱烷、立方烷(珠立方)，以及金二十的正四面體結構。

搭建珠串張力分子模型的基本步驟為「交叉連結」。如下圖兩條四珠串所示，將這兩條四珠串沿中間的珠隙彼此交叉，然後放鬆，彈性繩內的預應力所產生的拉力，讓珠子緊蹦在一起，環繞在交叉位置的四個珠子，其球心位置以正四面體的排列方式。

立方烷是一種籠形碳氫化合物，分子式為C8H8，其碳原子位在正立方體的八個頂點， 每一個碳原子連接到相鄰的三個碳原子與指向外側的氫原子。立方烷的價球模型中的 灰球代表組成碳碳單鍵的電子對，而白球則是組成碳氫鍵的電子對。

Schwarz D ("Diamond") minimal surface

Two students, 張皓 and 李于婕, in the class, Molecular Aesthetics 2020, recreated a bead model of Schwarz D ("Diamond") triply periodic minimal surface with 6mm black beads.

PKU-12 (Zeolite -CLO)

I constructed a bead model of PKU-12 (zeolite framework type -CLO) as a gift to Peking university in Dec. 2015. PKU-12 was synthesized by the team led by Profs. Yingxia Wang and Jianhua Lin. The details of their work is given in the paper entitled "A silicogermanate with 20-ring channels directed by a simple quaternary ammonium cation" published in Dalton Trans., 2013, 42, 1360.



The background of this photo is the Chemistry department of National Taiwan University and the beautiful Lake Moon-Drunk (or Lake Zui-Yue).

In my class, Molecular Aesthetics 2020, a student reproduced this model with different kind of beads.

Concentric carbon nanotori - a molecular gyroscope (Molecular Aesthetics 2020)