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S. Negami conjectured in $1988$ that a connected graph has a finite planarcover if and only if it embeds in the projective plane. It follows from theworks of D. Archdeacon, M. Fellows, P. Hlin\v{e}n\'{y}, and S. Negami that thisconjecture is true if the graph $K_{1, 2, 2, 2}$ has no finite planar cover. Weprove a number of structural results about putative finite planar covers of$K_{1,2,2,2}$ that may be of independent interest. We then apply these resultsto prove that $K_{1, 2, 2, 2}$ has no planar cover of fold number less than$14$.

$K_{1,2,2,2}$ has no $n$-fold planar cover graph for $n<14$