I need a spaceship habitat for a million humans, comfortably, for indefinite time.
I have read many questions around here, perfectly answered, about the size a spaceship should be to store enough technology to feed a million people indefinitely. I read about a spaceship which would be a cylinder half a mile wide and a mile long which will include entertainment for roughly 500 people, but not including creating new food.
I would like to expand this further.
By comfortably, I mean with enough space and variety to avoid psychological problems for a lifetime, not locked up in a prison with 20m^2 rooms.
I want a place where enough veggies could be farmed to not only sustain humans but also feed animals to be used as livestock. A place where people can actually "take a walk".
Basically I need a spaceship which could make these people not to regret leaving Earth, even in the hypothesis of never ever finding a suitable planet to land upon.
Making my personal computations, which are very childish, I came upon a sphere (best shape to prevent heat dispersion and to move in space) with around 4 miles radius. Rotating, obviously, to create artificial gravity.
But I will welcome completely different results.
If you think a sphere is not the best shape to move in space and prevent heat dispersion, or to place the thrusters, notify me. If you think no material, ever, not even in 5 centuries, will be able to prevent a structure such size from collapsing while accelerating or to resist minor debris impact, notify me. If you think my numbers are stupid, notify me. If you know there's no way getting enough oxygen, notify me. If you think there's no way getting enough energy for supports and thrusters, tell me.
Basically, as the very beginning of my question, I want a spaceship habitat (so not a human cargo) for a million humans for indefinite time.
Just hard science, given 500 years of human development.