The E7 commuting squares produce D10 as principal graph

We prove that the (two) connections, or commuting squares, on the Coxeter-Dynkin diagram E7 produce a subfactor with principal graph D10. This was conjectured by J.-B. Zuber in connection with modular invariants in conformal field theory, and solve the last case of computing the flat parts of the connections on Coxeter-Dynkin diagrams with index less than 4