If the spaceship is in the shape of a rotating glome, the rotation will inevitably settle into a Clifford double rotation where there are an infinite number of stationary plane. Or, put another way, if you trace each point of the glome as it rotates, it will trace out the Hopf fibration of the 3-sphere. Every point rotates in exactly the same way as every other point, so all points on the glome are equivalent, and will undergo the same centrifugal force. So the entire inside of the glome will have equal artificial gravity (under the centrifugal force), and will be completely habitable, unlike the 3D case where points close to the axis of rotation will have weaker artificial gravity.
The only problem with this kind of spaceship, though, is that
every point of the glome is undergoing rotation, so there is no fixed facing direction! The bridge would not remain facing the same direction, and neither will the thrusters. The glome itself will, of course, travel in a fixed overall direction, but none of its points will remain facing in this direction. So it will be very confusing for a pilot to steer the ship (the view is constantly rotating away from the direction of travel!), and rather tricky for thrusters to fire in the right direction (they are constantly rotating away from the direction they need to fire in!).
So it seems that such an arrangement would be more suitable as a stationary bio-glome than a space
ship. (In fact, if such a thing could arise naturally, then it would serve as the perfect replacement for 4D planets.
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