Chuang and I are particularly interested in toroidal shape of graphitical structures or carbon donuts. Systematic structural rules of this type of molecules have been worked out by us. The details were presented in these two articles:
1. "Generalized Classification Scheme of Toroidal and Helical Carbon Nanotubes." J. Chem. Inf. Model. 2009, 49, 361-368.
2. "Dual Space Approach to the Classification of Toroidal Carbon Nanotubes." J. Chem. Inf. Model. 2009, 49, 1679-1686.
We have made many bead models for carbon donuts. Here are a few models for isomers of TCNT (Toroidal carbon nanotube) with 240 carbon atoms. Since beads stand for carbon-carbon bonds (edge of the graph), one need 360 beads to create one such structure. The basic construction procedure is basically the same for all TCNTs. The difference is where and when to put a heptagons and pentagons for a particular TCNT.
(Constructed by Chuang)