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Yeah, the 3D klein bottle is to a real 4D klein bottle what a circle is to a sphere.


IE, cross-sections or projections. Would be interesting if there were a way to render a Klein bottle using techniques similar to those used when 'impossible triangles' are modeled with boards and 2x4s in fields which then seem to work when viewed from a certain angle. But then what would non-intersecting intersecting lines look like. Sounds like double-think.




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