it is also the intersection of a 6-cube with the hyperplane that bisects the 6-cube's long diagonal orthogonally. in this sense it is the 5-dimensional analog of the regular hexagon, octahedron, and bitruncated 5-cell. this characterization yields simple coordinates for the vertices of a birectified 5-simplex in 6-space: the 20 distinct permutations of (1,1,1,−1,−1,−1).