  In this article we study a VOA with two Miyamoto involutions generating
$S_3$. In \cite{M3}, Miyamoto showed that a VOA generated by two conformal
vectors whose Miyamoto involutions generate an automorphism group isomorphic to
$S_3$ is isomorphic to one of the four candidates he listed. We construct one
of them and prove that our VOA is actually the same as $\mathrm{VA}(e,f)$
studied by Miyamoto. We also show that there is an embedding into the moonshine
VOA. Using our VOA, we can define the 3A-triality in the Monster.
