by NeatNit » Mon Apr 22, 2019 6:21 pm
(bump!)
The simplest way I can think of is to not have the hole cut in the intersection. That way there is, in fact, an inside and an outside, with no way to get from one to the other (save for an inflation hole presumably installed). Arguably it misses the point of being a Klein bottle, being nothing more than a weirdly-shaped beach ball, but to some extent all 3D Klein bottles are compromises anyway because of this intersection so I'm not that worried about it.
Surprisingly, a Google search for "inflatable Klein bottle" finds nothing relevant! I think it's likely that someone has tried that, so it's likely that it doesn't work, i.e. isn't rigid enough or doesn't look very good when inflated. What a shame. I'd be happy to be proven wrong though!
Link to the comic:
https://www.smbc-comics.com/comic/topology
(bump!)
The simplest way I can think of is to not have the hole cut in the intersection. That way there is, in fact, an inside and an outside, with no way to get from one to the other (save for an inflation hole presumably installed). Arguably it misses the point of being a Klein bottle, being nothing more than a weirdly-shaped beach ball, but to some extent all 3D Klein bottles are compromises anyway because of this intersection so I'm not that worried about it.
Surprisingly, a Google search for "inflatable Klein bottle" finds nothing relevant! I think it's likely that someone has tried that, so it's likely that it doesn't work, i.e. isn't rigid enough or doesn't look very good when inflated. What a shame. I'd be happy to be proven wrong though!
Link to the comic: https://www.smbc-comics.com/comic/topology