  We extend a classification of irreducible, almost-commutative geometries
whose spectral action is dynamically non-degenerate, to internal algebras that
have six simple summands. We find essentially four particle models: An
extension of the standard model by a new species of fermions with vectorlike
coupling to the gauge group and gauge invariant masses, two versions of the
electro-strong model and a variety of the electro-strong model with Higgs
mechanism.
