Tori without latitudes?

Previously, I posted a picture of a beaded torus belonging to another family of toroidal carbon nanotubes which I claimed latitude coordinates do not exist. Therefore, I thought a new classification scheme is needed for this family of compounds. I wondered how long it will take before we figure out the algorithmic rule for them. Since this family also contains important systems of great interests, such as armchair-type toroidal nanotubes. It is imperative that we need to work out the systematic generating rules. Fortunately, it didn't take much time for Chern Chuang to show that our generalized classification scheme is indeed general enough to cover this kind of toroidal system. Now we can probably claim all existing toroidal carbon nanotubes have well-defined latitude coordinates. The details will be discussed in his thesis. Here are two beaded models he just constructed.