 The hypersimplex with parameters ("d",1) is a ("d" − 1)-simplex, with "d" vertices.The hypersimplex with parameters (4,2) is an octahedron, and the hypersimplex with parameters (5,2) is a rectified 5-cell.Generally, every ("k","d")-hypersimplex, Δ"d","k", corresponds to a uniform polytope, being the ("k" − 1)-rectified ("d" − 1)-simplex, with vertices positioned in the centers of all ("k" − 1)-face elements of a ("d" − 1)-simplex.