the "birectified 5-simplex" is the intersection of two regular 5-simplexes in dual configuration. the vertices of a birectification exist at the center of the faces of the original polytope(s). this intersection is analogous to the 3d stellated octahedron, seen as a compound of two regular tetrahedra and intersected in a central octahedron, while that is a first rectification where vertices are at the center of the original edges.