  A biconvex polytope is a classical and tropical convex hull of finitely many
points. Given a biconvex polytope, for each vertex of it we construct a
directed bigraph and a gammoid so that the collection of base polytopes of
those gammoids is a matroid subdivision of the hypersimplex, thereby proving a
biconvex polytope arises as a cell of a tropical linear space. Our construction
provides manually feasible guidelines for subdividing the hypersimplex into
base polytopes, without resorting to computers. We work out the rank-4 case as
a demonstration. We also show there is an injection from the vertices of any
(k-1)-dimensional biconvex polytope into the degree-(k-1) monomials in k
indeterminates.
