  This paper provides a complete list of Krajewski diagrams representing the
standard model of particle physics. We will give the possible representations
of the algebra and the anomaly free lifts which provide the representation of
the standard model gauge group on the fermionic Hilbert space. The algebra
representations following from the Krajewski diagrams are not complete in the
sense that the corresponding spectral triples do not necessarily obey to the
axiom of Poincare duality. This defect may be repaired by adding new particles
to the model, i.e. by building models beyond the standard model. The aim of
this list of finite spectral triples (up to Poincare duality) is therefore to
provide a basis for model building beyond the standard model.
