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What is the smallest convex set containing $8$ vertices of a hollow cube in $R^{3}$?

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    Can you please justify this termenology? Thanks in advance!2012-04-07

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$\{\sum_{i=1}^{8} \lambda_i v_i | \lambda_i \geq 0, \sum_{i=1}^{8} \lambda_i=1\}$, where $v_i$ are the vertices of the hollow cube.