A Klein bottle. I ran into this term on the web, and decided to find out what it really meant. I've visited a few pages, and I can't, for the life of me, figure out what it is! It's really hurting trying to understand.
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I remember reading that it can't exist in our world, and that we can only demonstrate it with 3-d models, just as we show 3d objects with 2-d pictures.
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Sure it can exist. Just like a mobius strip exists. I think what you might have in mind are higher dimensional objects that we can model in two or three dimensions but can really never percieve (google tesseract).
I think things like mobius strips and klien bottles were only concieved as a dirty trick to give mathematicians a headache.