Conjecture that LS-function combinatoric polytopes are simple

Let an LS function determine a combinatoric polytope obtained from its associated scattering-form or kinematic-space construction. Simplicity conjecture. All combinatoric polytopes obtained from LS functions are simple polytopes. This concerns the expected combinatorial structure of polytopes associated with general leading singularity cases; the source presents it as supported by evidence, while systematic constructions for general LS cases remain open.