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

Take any $d+3$ points in ${\mathbb{R}}^d$. 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).