  By a result of Mukai, the non-abelian Brill-Noether locus X = M_C(2,K:3F) of
type II, defined by a stable rank 2 vector bundle F of invariant 3 over a plane
quartic curve C, is a prime Fano 3-fold X of degree 16. The associate ruled
surface S^X = P(F) is uniquely defined by X, and we see that for the general X
= X_{16}, S^X is isomorphic to the Fano surface of conics on X. The argument
uses the geometry of the Sp_3-grassmannian and the double projection from a
line on X_{16}.
