I think the flat version is a more authentic representation of the 4-dimensional object. If you were a 2D creature embedded in the surface of a Klein bottle, s

I think the flat version is a more authentic representation of the 4-dimensional object. If you were a 2D creature embedded in the surface of a Klein bottle, space would seem flat in every direction... at least until you went out for a walk and found the mirror-image of your house.