  It has been shown by Hacking and Prokhorov that if the projective surface X
with quotient singularities and self-intersection number 9 has a smoothing to
the projective plane, then X is the general fiber of a Q-Gorenstein deformation
of the weighted projective plane with weights giving solutions to the Markov
equation. This result has been understood and generalized by combinatorial
mutations of Fano triangles by Akhtar, Coates, Galkin, and Kasprzyk. In this
note, we study this result by utilizing polarized T-varieties and describe the
associated deformation explicitly in terms of certain Minkowski summands of
so-called divisorial polytopes.
