The elementary particles of the Standard Model seem clearly enumerated and distinguished, totaling 17 (6 quarks, 6 leptons, 4 gauge bosons, and the Higgs). Is there a similar enumeration of the variety of fundamental interactions found in nature according to the Standard Model? If it is finite, how many particular interactions are there (ie, in terms of the 17 elementary particles), and is every such interaction expressible as a Feynman Diagram? Thanks.
EDIT: To clarify, I was asking about how many total interactions like ($e^- + e^+ \rightarrow \mu^- + \mu^+$) and ($e^- \rightarrow e^- + \gamma$) there are.
EDIT2: The Wikipedia article on "Fundamental interaction" says: "The interaction of any pair of fermions in perturbation theory can then be modelled thus: Two fermions go in --> interaction by boson exchange --> Two changed fermions go out." This seems to imply that the total number of possible interactions is $N(N-1)/2$ (if interactions of like particles are excluded). Since there are 12 fermions, the number of interactions amounts to 66. Are all such interactions found in nature?