Geometrical CP violation from non-renormalisable scalar potentials

We consider in detail the non-renormalisable scalar potential of three Higgs doublets transforming as an irreducible triplet of Δ(27) or Δ(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.