Is there something about the repulsion of the lone pair on thenitrogen that prevents the cyanides being all on the same plane?
Use crystal field theory. You have a 3d⁷ metal with four strong field ligands. If you compare the tetrahedral and square planar geometries for this case, you should find that square planar gives a larger CSFE because of the big Δ.
Simply by using 3-rank Contravariant or Covariant Tensor of coordinates of Riemann Geometry cyanide ligands are to be formed Cobalt 2+ion.
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