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dimensions, other relations among the numbers of faces of a polytope become important as well, including the Dehn-Sommerville equations which, expressed in terms of ''h''-vectors of simplicial polytopes, take the simple form h_k = h_{d - k} for all k. The instance of these equations with k = 0 is equivalent to Euler's formula but for d > 3 the other instances of these equations are linearly independent of each other and constrain the h-vectors

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