  Let $P_n$ denote the $n$-th linear ordering polytope. We define projections
from $P_n$ to the $n$-th permutahedron and to the $(n-1)$-st linear ordering
polytope. Both projections are equivariant with respect to the natural
$\Sn$-action and they project to orthogonal subspaces. In particular the second
projection defines an $S_n$-action in $P_{n-1}$.
