  We consider in detail the non-renormalisable scalar potential of three Higgs
doublets transforming as an irreducible triplet of Delta(27) or Delta(54). We
start from a renormalisable potential that spontaneously leads to a vacuum with
CP-violating phases independent of arbitrary parameters - geometrical CP
violation. Then we analyse to arbitrarily high order non-renormalisable terms
that are consistent with the symmetry and we demonstrate that inclusion of
non-renormalisable terms in the potential can preserve the geometrical
CP-violating vacuum.
