2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230396Refereed version to appear in Michigan Mathematical Journal. A mistake in the last section of the previous version has been corrected. The new title exactly describes the main result obtained. Building on the geometry of cubic surfaces and on a theorem of Dolgachev, the rationality of the moduli space R mentioned in the title is proved. Let M be the moduli space of 6 points in the plane, modulo the natural involution induced by double-six configurations on cubic surfaces. It is proved that R is birational to a tower of locally trivial projective bundles ending onto M. The rationality of R then follows from Dolgachev's theorem that M is rational.19 pages. Section 2 replaced by the final one. Further restyling. Same contentsAlgebraic Geometry14H45, 14H10text