  Within multi-Higgs-doublet models, one can impose symmetries on the Higgs
potential, either discrete or continuous, that mix several doublets. In
two-Higgs-doublet model any such symmetry can be conserved or spontaneously
violated after the electroweak symmetry breaking (EWSB), depending on the
coefficients of the potential. With more than two doublets, there exist
symmetries which are always spontaneously violated after EWSB. We discuss the
origin of this phenomenon and show its similarity to geometric frustration in
condensed-matter physics.
