  Perfect colourings of the rings of cyclotomic integers with class number one
are studied. It is shown that all colourings induced by ideals (q) are chirally
perfect, and vice versa. A necessary and sufficient condition for a colouring
to be perfect is obtained, depending on the factorisation of q. This result
yields the colour symmetry group H in general. Furthermore, the colour
preserving group K is determined in all but finitely many cases. An application
to colourings of quasicrystals is given.
