  We prove that a face of a cube can be optimally partitioned into connected
193 sets on which the cut locus, or ridge tree, is constant up to isomorphism
as a labeled graph. These are 60 connected open sets, curves bounding them, and
intersection points of curves. Polynomial equations for the curves are
provided. Sixteen pairs of sets support the same cut locus class. We present
the 177 distinct cut locus classes.
