  We give a complete enumeration of all 2-neighborly $d$-polytopes with $d+9$
and less facets. All of them are realized as 0/1-polytopes, except a 6-polytope
$P_{6,10,15}$ with 10 vertices and 15 facets, and pyramids over $P_{6,10,15}$.
In particular, we update the lower bounds for the number of facets of a
2-neighborly $d$-polytope $P$ and showed that the number of facets of $P$ is
not less than the number of its vertices $f_0(P)$ for $f_0(P) \le d + 10$.
