If the universe is more or less an infinite sphere in shape, would future space travel refer to different areas as quadrants like in Star Trek? Would cubed mapping be efficient for a spherical domain? #notenoughcoffeetoday

I think you end up with quadrents because navigation in Star Trek is based on two planes. 360 degrees horizontally and 360 vertically, relative to a point in space. There's probably a much better explanation somewhere in a Technical Manual...