  It is proved that every discrete Morse function in the sense of Forman on a
finite regular CW complex can be represented by a polyhedral Morse function in
the sense of Banchoff on an appropriate embedding in Euclidean space of the
barycentric subdivision of the CW complex; such a representation preserves
critical points. The proof is stated in terms of discrete Morse functions on a
class of posets that is slightly broader than the class of face posets of
finite regular CW complexes.
