  In a previous paper (Corrigan-Sasaki), many remarkable properties of
classical Calogero and Sutherland systems at equilibrium are reported. For
example, the minimum energies, frequencies of small oscillations and the
eigenvalues of Lax pair matrices at equilibrium are all "integer valued". The
equilibrium positions of Calogero and Sutherland systems for the classical root
systems (A_r, B_r, C_r and D_r) correspond to the zeros of Hermite, Laguerre,
Jacobi and Chebyshev polynomials. Here we define and derive the corresponding
polynomials for the exceptional (E_6, E_7, E_8, F_4 and G_2) and
non-crystallographic (I_2(m), H_3 and H_4) root systems. They do not have
orthogonality but share many other properties with the above mentioned
classical polynomials.
