There are at most 2^(d+1)-2 neighbourly simplices in dimension d
classification
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neighbourlysimplicestherecombinatorialcubedimensiondiscretedisjoint
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A combinatorial theorem on families of disjoint sub-boxes of a discrete cube, which implies that there at most $2^{d+1}-2$ neighbourly simplices in $\mathbb R^d$, is presented.
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