  Refereed 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.
