The diameter of the ridge-graph of a cyclic polytope

It is shown that the diameter of the the ridge-graph, that is, the graph of the polytope $C^*(d,n)$ dual to the given polytope, where $d$ is the dimension and $n$ is the number of facets of the polytope, is equal to $n-d-\max\{0,\lceil(n-2d)/(\lfloor d/2\rfloor+1)\rceil\}$.