  Stringy canonical forms are a class of integrals that provide
$\alpha'$-deformations of the canonical form of any polytopes. For generalized
associahedra of finite-type cluster algebra, there exist completely rigid
stringy integrals, whose configuration spaces are the so-called binary
geometries, and for classical types are associated with (generalized)
scattering of particles and strings. In this paper we propose a large class of
rigid stringy canonical forms for another class of polytopes, generalized
permutohedra, which also include associahedra and cyclohedra as special cases
(type $A_n$ and $B_n$ generalized associahedra). Remarkably, we find that the
configuration spaces of such integrals are also binary geometries, which were
suspected to exist for generalized associahedra only. For any generalized
permutohedron that can be written as Minkowski sum of coordinate simplices, we
show that its rigid stringy integral factorizes into products of lower
integrals for massless poles at finite $\alpha'$, and the configuration space
is binary although the $u$ equations take a more general form than those
"perfect" ones for cluster cases. Moreover, we provide an infinite class of
examples obtained by degenerations of type $A_n$ and $B_n$ integrals, which
have perfect $u$ equations as well. Our results provide yet another family of
generalizations of the usual string integral and moduli space, whose physical
interpretations remain to be explored.
