Background:
There are those "infinite puzzles" that map the view of our galaxy to the surface of a Klein bottle (https://n-e-r-v-o-u-s.com/blog/?p=7613) or a real projective plane (https://n-e-r-v-o-u-s.com/blog/?p=8068). To my understanding the original image is a 360 degrees view of our galaxy. So that is equivalent to an image on the inner surface of a sphere.
My Question:
What I can't understand: How do you map such an image to the surface of a Klein bottle or a real projective plane without getting any artifacts (like the image is not correctly tiling)?
Did I misunderstood anything?
Did they used any tricks?
Beware: I have no real knowledge about topology, so please try to use common language in any explanation. (As I am not sure which tag fits best, I also added multiple "similar sounding"(to my ears))