Boolean quadric polytopes are faces of linear ordering polytopes

Let $P_{\mathrm{BQP}}(n)$ be a boolean quadric polytope, $n\in\mathbb{N}$, $P_{\,\mathrm{LO}}(m)$ — linear ordering polytope, $m\in\mathbb{N}$. It is shown that $P_{\mathrm{\,BQP}}(n)$ is affine equivalent to a face of $P_{\,\mathrm{LO}}(2n)$.