Wednesday, June 18, 2008

Two tori with five- and six-fold rotation axes, respectively

The two tori, denoted by T5 and T6, in the following picture have C5 an C6 rotational symmetry axes, respectively. The one with C5 axis has 240 carbon atoms (360 beads used). There are 10 pairs of 5-7gons for T5 and 12 pairs for T6. Roughly speaking, the tubule direction will be changed by 36 (30) degrees for T5 (T6), whenever a 5-7 pair is introduced. But, in the middle of a real weaving process when the two ends of tubule has not been connected, I found that the actual bending angle due to a single 5-7 pair is in between these numbers. This indicates that both kinds of tori have extra bending energies not coming from the 5-7 pairs. Curiously, it seems to me the actual molecular modeling supports this observation.

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