An example of an "unlinked" set of 2k + 3 points in 2k-space

Take any d + 3 points in Rᵈ. It is known that (a) if d = 2k + 1, then there are two linked (k + 1) -simplices with the vertices at these points; (b) if d = 2k, then there are two disjoint (k + 1) -tuples of these points such that their convex hulls intersect. The analogue of (b) for d = 2k + 1, which is also the analogue of (a) for intersections (instead of linkings), states that there are two disjoint (k + 1) - and (k + 2) -tuples of these points such that their convex hulls intersect. This analogue is correct by (a).