Here is the list of stable isomers of T240. According to Chuang's generation algorithm for the toroidal compounds, there are 40 isomers for T240. By simple inspection, I think more than half of them are probably unstable, particularly those with very large radius and very small girth. If chiral compounds are not counted twice, there are 14 isomers. These stable isomers can be classified into five type based on the arrangement of heptagons in the inner-rim as shown in the following figures.
Currently, I have created the beaded models for 12 of them. Only I5 and II5 are missing. This kind of isomers is related to their parent isomers, I1 and II1 by twisting the upper and lower parts of the torus respectively.
According to my previous experience, the isomers generated by this kind of transformation seem to be quite unstable as shown in one of my previous post. But the calculation based on Chuang's simple force field suggests that this kind of isomers could sometimes be stable depending on the type of inner-rim.
No beaded models for I5 and I6.
No beaded models for II5 and II6.
The tori in these figures are generated by the matlab scripts written by Chuang Chern, possibly with many useful discussions with Fan Yuan-Jia.