Do rotations of one point around all arbitrary axes form a sphere? Correct me if I am wrong but assume I have a point in 3D which I would like to rotate around all arbitrary axes fixed at common origin. Then this is true that all orbits circled by rotated point will form an empty sphere of radius equal to the distance between point and origin? If I am right could you give me some references. Just in case to explore why my intuition is correct.

Consider the sphere centered at the origin and extending to the point. Consider any other point on that sphere. Consider the great circle connecting the two points. Make believe that great circle is the Equator. Then a rotation around the axis through the North and South Poles wil take the one point to the other. 
