I have to proof the following thing:
Show that all empty symplices ( i.e a subset of the complex T s.t T is not inside but all the subset are inside T) in the boundary complex of $cyc_{2d}(n)$ have size $d+1$.
As $cyc_{2d}(n)$ is $d$ neighborly I could show that all subsets of size smaller or equal to $d$ cannot be a empty simplex. I still need to show that all subsets of size $\geq d+2$ cannot form a empty simplex. Why is this true?