In addition to the eight structural types of carbon nanotori, Chern also showed that there are five other different tori without latitude coordinates defined. Chern also gave the systematic transformation rule, which we call the generalized Stone-Wells transformation, to derive them from classes A, B, and E, respectively.
Mr. Horibe has made many different structural types of tori with beads as shown in the following photo taken in the Nagoya's Children and Family Center. One can see he enjoyed making tori with 7- up to 9-fold rotational symmetry quite a lot.
However, I didn't check very carefully how many different types of tori (according to our classification scheme) he has done.
I also discovered that
he has a few tori without latitude coordinates.
Incidentally, I found that Mr. Horibe had made a particular torus which is exactly the same as the one (class K) that appeared in one of slides of my introductory talk given in the Nagoya's Children and Family Center. Even the color codings are the same. Quite amazing.