  The chromatic number related to a colouring of facets of certain classes of
generalised associahedra is studied. The exact values are obtained for
permutohedra, associahedra and simple permutoassociahedra, while lower and
upper bounds are established for cyclohedra and stellohedra. The asymptotic
values of the chromatic numbers for associahedra, cyclohedra and simple
permutoassociahedra are given.
