2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64510In 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.latex 26pages, new sections on simple current extensions and embedding into the moonshine VOA are addedQuantum Algebra17B68, 17B69text