Here is something mind bending.
Closed loops can be knotted (knot theory) in 3D. If the analogy is correct, closed 2D surfaces can be knotted in four dimensions: sphere, torus, Klein bottle, etc. (I think the Klein bottle may be constructed without self intersecting surfaces in 4D. )
Even more mindbendingly, these knotted surfaces can be unknotted in five dimensions. Closed loops in 3D may be unknotted in 4D.
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