  Using tropical convexity Dochtermann, Fink, and Sanyal proved that regular
fine mixed subdivisions of Minkowski sums of simplices support minimal cellular
resolutions. They asked if the regularity condition can be removed. We give an
affirmative answer by a different method. A new easily checked sufficient
condition for a subdivided polytope to support a cellular resolution is proved.
The main tool used is discrete Morse theory.
