Jahn-Teller effects can result in 'pseudorotation', which is rotation of a distortion. This should not be confused with rotation of a real molecule. An example for C60 is illustrated below. One carbon atom has been coloured red to guide the eye (thanks to Prof. Janette Dunn for providing the images).
Note how the shape of the distortion rotates clockwise but the atom coloured red simply moves up and down. This is further shown by the snapshots below.
Note how the atom coloured red rotates around as the shape of the distortion rotates. This is also shown by the snapshots below.