  Motivated by discrete flavour symmetry models, we analyse Spontaneous CP
Violation (SCPV) for potentials involving three or six Higgs fields (both
electroweak doublets and singlets) which fall into irreducible triplet
representations of discrete symmetries belonging to the $\Delta(3n^2)$ and
$\Delta(6n^2)$ series, including $A_4$, $S_4$, $\Delta(27)$ and $\Delta(54)$.
For each case, we give the potential and find various global mimima for
different regions of the parameter space of the potential. Using CP-odd basis
Invariants that indicate the presence of Spontaneous CP Violation we separate
the VEVs into those that do or do not violate CP. In cases where CP is
preserved we reveal a CP symmetry of the potential that is preserved by those
VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify
interesting cases where there is Spontaneous Geometrical CP Violation in which
the VEVs have calculable phases.
