The adiabatic potential surface for icosahedral systems having three-, four-and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v, U-v and V-v problems) is investigated. It is shown that for the T-v and V-v Jahn-Teller cases the potential surface possesses respectively a twoor three-dimensional equipotential continuum of minima. For the U-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on 1;he adiabatic potential surfaces is elucidated. In the linear approximation to the V-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.
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