The Mirror of the Cubic Surface

A number of years ago, one of us (Mark Gross) was giving a lecture at the University of Warwick on the material on scattering diagrams from [GPS10]. Of course, Miles was in the audience, and he asked (paraphrasing as this was many years ago) whether, at some point, the lecturer would come back down to earth. The goal of this note is to show, in fact, we have not left the planet by considering a particularly beautiful example of the mirror symmetry construction of [GHK15b], namely the mirror to a cubic surface.