If you disagree with the terminology, that's your opinion. A lot of terminology is kind of weird. "Klien Bottle" is called that because it was called "Klien Sur

If you disagree with the terminology, that's your opinion. A lot of terminology is kind of weird. "Klien Bottle" is called that because it was called "Klien Surface" in German, but "Surface" in German kind of sounds like "Flask", and they mistranslated. The name stuck because it was kind of appropriate. I say it's a 2D surface, because while it lives in 3D, it's "thin" in one dimension. It's like saying a piece of paper is a 2D object. And when I say "it can't live in 2D", I'm kind of lying - it can live in a weird kinky 2D space, but NOT a boring 2D plane. Well, you could smash it into a 2D plane, but it would self-intersect (get all smushed together, losing its shape). And by "shape", I mean topological properties ... but I hate jargon. But a Mobius strip is a 2D surface which can't live in 2D (a boring flat 2D plane); in the same way a Klien Flask is a 2D surface which can't live in 3D; and a knot is a 1D surface which can't live in 1 or 2D. Press a knot into 2D, and it crosses itself (self-intersect). Force a knot into 2D, and it will break, or join up with itself (depending on the material). Real mathematicians (i.e. not me) will say "manifold", not surface, but it's more or less the same thing.