  Let $Z\subset Fl(n)$ be the closure of a generic torus orbit in the full flag
variety. Anderson-Tymoczko express the cohomology class of $Z$ as a sum of
classes of Richardson varieties. Harada-Horiguchi-Masuda-Park give a
decomposition of the permutohedron, the moment map image of $Z$, into
subpolytopes corresponding to the summands of the Anderson-Tymoczko formula. We
construct an explicit toric degeneration inside $Fl(n)$ of $Z$ into Richardson
varieties, whose moment map images coincide with the HHMP decomposition,
thereby obtaining a new proof of the Anderson-Tymoczko formula.
