Currently, the set of rotopes includes rotatopes, toratopes and tapertopes. As you should know, the extensions to the rotope construction system caused the introduction of so-called ambiguous, immeasurable and strange rotopes. Strange rotopes have of course been given a proper definition after their discovery but I would like to disclaim the other two sets, as they are just about useless.
Doing this without disturbing the process of rotopic construction is more or less impossible. Therefore I would like to split the set of rotopes up into the following two sets:
- Toratopes. PWrong's recent research has brought more importance to the set of closed toratopes itself, so it deserves to be standalone and lose the "closed" qualifier (which would then be implicit). This set does of course include the so-called strange rotopes as there is nothing truly strange about them; the "strange" attribute would be dropped as well.
- Tapertopes. The new definition of tapertopes would be "any combination of Cartesian product and pyramid operations on hyperspheres." Therefore, with this definition, there are some shapes that would (and deserve to) appear in this set which were not in the original set of rotopes, such as the 3-3 duoprism. Cylinders (and variations thereof) would also appear in this set.
- ambiguous and immeasurable rotopes, which would be disclaimed
- Cartesian products of non-hyperspheric closed toratopes and rotopes. Unless anyone has any better ideas, it seems a worthy compromise to not include these in either set. In 4D, the only instance of this is the torinder; there are more in 5D and higher.
If anyone has any objections to this, please say so. If I don't receive any objections in a week (i.e. by the 26th), I'll update the entire wiki to reflect the changes, archiving the old information. I hope you all see why I am proposing this change and how it would simplify a lot of concepts related to rotopes.