The coarsest hyperplane subdivisions of the permutahedron into Bruhat interval polytopes from lattice path matroid flags are the only such subdivisions and arise from points in the complete nonnegative flag variety.
Selected papers based on the presentations at the workshop, Magdeburg, Germany, September 14–16, 2017, Cham: Springer, 2022, pp
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On subdivisions of the permutahedron and flags of lattice path matroids
The coarsest hyperplane subdivisions of the permutahedron into Bruhat interval polytopes from lattice path matroid flags are the only such subdivisions and arise from points in the complete nonnegative flag variety.