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We continue the study of positive geometries underlying the {\it Grassmannianstring integrals}, which are a class of "stringy canonical forms", or stringyintegrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. Theleading order of any such stringy integral is given by the canonical functionof a polytope, which can be obtained using the Minkowski sum of the Newtonpolytopes for the regulators of the integral, or equivalently given by theso-called scattering-equation map. The canonical function of the polytopes forGrassmannian string integrals, or the volume of their dual polytopes, is alsoknown as the generalized bi-adjoint $\phi^3$ amplitudes. We compute all thelinear functions for the facets which cut out the polytope for all cases up to$n=9$, with up to k=4 and their parity conjugate cases. The main novelty of ourcomputation is that we present these facets in a manifestly gauge-invariant andcyclic way, and identify the boundary configurations of $G_+(k,n)/T$corresponding to these facets, which have nice geometric interpretations interms of $n$ points in $(k{-}1)$-dimensional space. All the facets andconfigurations we discovered up to $n=9$ directly generalize to all $n$,although new types are still needed for higher $n$.

Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals