  Some widely known compact extended formulations have the property that each
vertex of the corresponding extension polytope is projected onto a vertex of
the target polytope. In this paper, we prove that for heptagons with vertices
in general position none of the minimum size extensions has this property.
Additionally, for any d >= 2 we construct a family of d-polytopes such that at
least 1/9 of all vertices of any of their minimum size extensions is not
projected onto vertices.
