Thursday, June 25, 2015

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.

Friday, May 15, 2015

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.

Saturday, May 2, 2015

Wednesday, April 29, 2015

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.