  Seiberg and Witten have shown that in N=2 SQCD with $N_f=2N_c=4$ the
S-duality group PSL(2,Z) acts on the flavor charges, which are weights of
Spin(8), by triality. There are other N=2 SCFTs in which SU(2) SYM is coupled
to strongly-interacting non-Lagrangian matter: their matter charges are weights
of $E_6$, $E_7$ and $E_8$ instead of Spin(8). The S-duality group PSL(2,Z) acts
on these weights: what replaces Spin(8) triality for the $E_6,E_7,E_8$ root
lattices?
  In this paper we answer the question. The action on the matter charges of (a
finite central extension of) PSL(2,Z) factorizes trough the action of the
exceptional Shephard--Todd groups $G_4$ and $G_8$ which should be seen as
complex analogs of the usual triality group $\mathfrak{S}_3\simeq
\mathrm{Weyl}(A_2)$.
  Our analysis is based on the identification of S-duality for SU(2) gauge
SCFTs with the group of automorphisms of the cluster category of weighted
projective lines of tubular type.
