 The one remaining graph for which this has not yet been done is "K"1,2,2,2, a seven-vertex apex graph that forms the skeleton of a four-dimensional octahedral pyramid.If "K"1,2,2,2 could be shown not to have any planar covers, this would complete a proof of the conjecture.On the other hand, if the conjecture is false, "K"1,2,2,2 would necessarily be its smallest counterexample.