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In this paper we will classify the finite spectral triples with KO-dimensionsix, following the classification found in [1,2,3,4], with up to four summandsin the matrix algebra. Again, heavy use is made of Kra jewski diagrams [5].Furthermore we will show that any real finite spectral triple in KO-dimension 6is automatically S 0 -real. This work has been inspired by the recent paper byAlain Connes [6] and John Barrett [7].  In the classification we find that the standard model of particle physics inits minimal version fits the axioms of noncommutative geometry in the case ofKO-dimension six. By minimal version it is meant that at least one neutrino hasto be massless and mass-terms mixing particles and antiparticles are prohibitedComment: Revised version for publication in the Journal of Mathematical  Physic

On a classification of irreducible almost-commutative geometries IV