Extendable shellability of dual hypersimplices

A hypersimplex is the matroid polytope of a uniform matroid, and its dual polytope is the polytope dual to that hypersimplex. A shelling is extendable if every partial shelling can be completed to a shelling of the whole polytope. The hypersimplex conjecture. The dual polytope of every hypersimplex is extendably shellable. This is presented as a geometric analogue of Simon's conjecture and as a potentially more tractable related problem; the source notes that the conjecture is unresolved and that its relation to extendable shellability of independence complexes is non-equivalent.