The face lattice of any simplicial polytope is Hamiltonian

Abstract: We show that the face lattice of any simplicial polytope is Hamiltonian. This proves a major part of a recent conjecture by \citeauthor{Listingfaces} which states that the face lattice of any polytope is Hamiltonian (SODA26). We use a line shelling in both directions to obtain two different decompositions of the face lattice into disjoint cubes, which allows the application of a theorem by Gregor to obtain the Hamilton cycle.