Eight structural types of TCNTs

Chern and I constructed many bead models of toroidal carbon nanotubes (TCNTs) in the last few years. We understand pretty well about the relationship among different kinds of TCNTs. Based on the spatial arrangement of 5- and 7-gons, we discovered that we can classify these achiral TCNTs into 8 structural types with well-defined latitudes and 5 other miscellaneous cases which may not have well-defined latitudes.

The eight bead models shown in the following photo are models for these eight canonical structural types.

Chern and I submitted a comment about the structural rules described in a paper by Beuerle et al to the "Chem. Eur. J." last May. After seven months of extensive review, which is much longer than the typical one to two months, our paper was rejected a few days ago.
The referee suggested us that

"A revised version of the manuscript, not criticizing the paper by Beuerle et al but instead providing a detailed and at the same time accessible account of the classification of TCNTs, might be suitable for a more specialized journal."

1. F. Beuerle, C. Herrmann, A. C. Whalley, C. Valente, A. Gamburd, M. A. Ratner, J. F. Stoddart, Optical and Vibrational Properties of Toroidal Carbon Nanotubes. Chem. Eur. J. 2011, 17, 3868-3875. See also Hot topic on carbon from Wiley-VCH.