 An alternative construction (for "k" ≤ "d"/2) is to take the convex hull of all ("d" − 1)-dimensional (0,1)-vectors that have either ("k" − 1) or "k" nonzero coordinates.This has the advantage of operating in a space that is the same dimension as the resulting polytope, but the disadavantage that the polytope it produces is less symmetric (although combinatorially equivalent to the result of the other construction).A hypersimplex Δ"d","k" is also the matroid polytope for a uniform matroid with "d" elements and rank "k".