A four dimensional object spinning on it's axis.

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A two-dimensional object, like a circle, has a zero-dimensional point that remains stationary while it spins. Similarly, a three-dimensional sphere has a one-dimensional line as its axis, where points on that line stay fixed during rotation. The discussion proposes that a four-dimensional sphere would have a two-dimensional plane as its axis. It also raises the question of whether an n-dimensional sphere would have an (n - 2)-dimensional axis. Additionally, the conversation touches on the concept of point-like particles and their inability to spin due to lacking dimensions to spin through.
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If a two dimensional object (say a circle) spins, their is a zero dimensional 'point' that stays in the same place as it spins.

If a three dimensional object (sphere?) spins on its axis, there is a one dimensional 'line' (its axis) such that any part of that sphere that lies on that line would stay in the same position in space.

If you spun an 4d 'sphere', then would there be a 2d plane that you could call its 'axis'?

And further, if you spun an n dimensional sphere, would its axis be (n - 2) dimensional?

Any comments would be good, thanks.

edit: is this why a point like particle cannot spin? i.e. they have no dimensions to spin through?

Does a negative number of dimensions have any meaning?
 
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Maybe you can think about the revolving sphere spinning on a 2nd axis such that the original axis sweeps out a plane. Hmm...
 

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