Isomorphic-vertex conjecture for critical banned graphs

Let a graph be critical banned in dimension $d$ when it is banned in dimension $d$ but deleting any vertex lowers the required dimension. Two vertices are isomorphic when deleting either one produces a graph of smaller dimension and the two resulting graphs are isomorphic. The isomorphic-vertex conjecture. Every graph critical banned in dimension $d$ has at least two isomorphic vertices. The source gives no proof or resolution.