I am not asking what a Klein bottle would look like if put in the 2 dimensions. I am asking about a 3D shape that in 2D would be like how a Klein bottle is to us in 3D.
I am mainly asking this to "visualize" how it would be for us if we went into the 4th dimension and saw a Klein bottle by using the the same situation but in 2D $\to$ 3D form since we can actually comprehend those dimensions.
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Yeah it's called a Mobius loop. Drift over to math-topology, and you'll see that various shapes are created by taking a rectangle (in 2-D space) and identifying various vertex pairs. You can end up with a bracelet (loop) or a Mobius strip; if you twist the vertex identifications even further, really interesting shapes result, a sphere being one of them.
I like to claim that, for 1-D space, the analogous object is a circle. I'm not certain whether that's mathematically correct.
The answer is simple. First, in two dimensions, imagine a flat plane with a bit of string lying on it. The string is not coiled up and resides entirely on the surface of the plane.
Now pick up the string and tie a simple knot in it. The knotted string can no longer live on the 2-D surface because to make the knot, the string has to leave the 2-D surface and become a 3-D object. A being that lives in the 2-D plane can follow the string up to the point where it leaves the plane- where it mysteriously disappears, only to mysteriously re-appear a short distance away from the knot.
You can also imagine a narrow 2-D strip of paper lying in the plane. You pick it up, put a half-twist into it and glue the ends together to make a Moebius strip. Because it has a twist through an extra dimension, it can no longer reside on a 2-D surface and if you smoosh it flat to do so- and then trace its length- you will find a spot where the strip crosses over itself. At that point, a 2-D being in the plane would see the strip nearing itself, and then disappearing suddenly where one part goes over the other, and then reappearing- with its left and right sides reversed.
In a 3-D world with a twist of the space through an extra dimension, you would see part of an object vanish into thin air and then reappear some distance away. If you stood between those two points and looked into one of them, you would see the back of your own head.