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If $K=\\{1,2,..., k\\}$ then the maximum number of the vertices of a complete graph that admits a biclique cover of type $K$ with $d$ bicliques, $n(k,d)$, is the maximum possible cardinality of a $k$-neighborly family of standard boxes in $\\mathbb{R}^d$.\n  In this paper, we obtain an upper bound for $n(k,d)$. 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