Shelling and triangulating the (extra)ordinary polytope

摘要: Ordinary polytopes were introduced by Bisztriczky as a (nonsimplicial) generalization of cyclic polytopes. We show that the colex order facets ordinary polytope is shelling order. This shares many nice properties with shellings simplicial also give shallow triangulation polytope, and how are used to compute toric h-vector polytope. As one consequence, we get contribution from each component nonnegative. Another consequence combinatorial proof entries any simple sums binomial coefficients.