There should be a spiral map for every player amount, such that any group of n player can play on a spiral galaxy with n arms, such that there are no empty arms.



Also, perfect balance should imply absolute equality not just in system placement but in system contents as well, aside from home planets of course.



This would be easiest to implement on spiral of course since it is just rotational symmetry.

I don't think that would make for a good game, maybe in MP setting but heck even there I wouldn't want perfect mirroring.



That's one of the biggest value factors and replay value of ES. You may get a wonderful start with great systems, but your neighbours won't, so they start hating on you and declare war. Or you get a crappy one with few good systems and are forced to expand etc.