  Margot (1994) in his doctoral dissertation studied extended formulations of
combinatorial polytopes that arise from "smaller" polytopes via some
composition rule. He introduced the "projected faces property" of a polytope
and showed that this property suffices to iteratively build extended
formulations of composed polytopes.
  For the composed polytopes, we show that an extended formulation of the type
studied in this paper is always possible only if the smaller polytopes have the
projected faces property. Therefore, this produces a characterization of the
projected faces property.
  Affinely generated polyhedral relations were introduced by Kaibel and
Pashkovich (2011) to construct extended formulations for the convex hull of the
images of a point under the action of some finite group of reflections. In this
paper we prove that the projected faces property and affinely generated
polyhedral relation are equivalent conditions.
