  In [Baumeister, H., Nill, Paffenholz, On permutation polytopes, Adv. Math.
222 (2009), 431-452 / arXiv:0709.1615] we conjectured a characterization of
subgroups H of a permutation group G so that, on the level of permutation
polytopes, P(H) is a face of P(G). Here we present the embarrassingly simple
proof of this conjecture.
