Answers at How to visualize a 4-dimensional parametric surface? give functions for producing images of 3D projections of 4D embeddings of the Klein bottle.
Is there a way to get such a 3D projection from a 4D embedding of the Klein bottle that is the customary "beer-bottle" surface used to help visualize the Klein bottle?
(For a strictly mathematical version of the question, see: https://math.stackexchange.com/questions/2946505/topological-embedding-of-klein-bottle-into-mathbbr4-that-projects-to-usual.)
Prior posts about 3D immersion of the Klein bottle do not help. I already know how to produce an image of that "standard" 3D immersion of the Klein bottle K. But as I said, I want to start with an explicit embedding function into 4D and then an explicit projection down to 3D whose image is that "beer-bottle" immersed surface.