  Calogero-Moser models can be generalised for all of the finite reflection
groups. These include models based on non-crystallographic root systems, that
is the root systems of the finite reflection groups, H_3, H_4, and the dihedral
group I_2(m), besides the well-known ones based on crystallographic root
systems, namely those associated with Lie algebras. Universal Lax pair
operators for all of the generalised Calogero-Moser models and for any choices
of the potentials are constructed as linear combinations of the reflection
operators. The consistency conditions are reduced to functional equations for
the coefficient functions of the reflection operators in the Lax pair. There
are only four types of such functional equations corresponding to the
two-dimensional sub-root systems, A_2, B_2, G_2, and I_2(m). The root type and
the minimal type Lax pairs, derived in our previous papers, are given as the
simplest representations. The spectral parameter dependence plays an important
role in the Lax pair operators, which bear a strong resemblance to the Dunkl
operators, a powerful tool for solving quantum Calogero-Moser models.
