  In this note, we study the permutohedral geometry of the poles of a certain
differential form introduced in recent work of Arkani-Hamed, Bai, He and Yan.
There it was observed that the poles of the form determine a family of
polyhedra which have the same face lattice as that of the permutohedron. We
realize that family explicitly, proving that it in fact fills out the
configuration space of a particularly well-behaved family of generalized
permutohedra, the zonotopal generalized permutohedra, that are obtained as the
Minkowski sums of line segments parallel to the root directions $e_i-e_j$.
  Finally we interpret Mizera's formula for the biadjoint scalar amplitude
$m(\mathbb{I}_n,\mathbb{I}_n)$, restricted to a certain dimension $n-2$
subspace of the kinematic space, as a sum over the boundary components of the
standard root cone, which is the conical hull of the roots $e_1-e_2,\ldots,
e_{n-2}-e_{n-1}$.
