  We define and study a family of cubic surfaces in the projectivized tangent
bundle over a four dimensional projective space associated to the root system
D_5. The 27 lines are rational over the base and we determine the classifying
map to the moduli space of marked cubic surfaces. This map has degree two and
we use it to get short proofs for some results on the Chow group of the moduli
space of marked cubic surfaces.
