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Let $P$ be a polyhedron in $\mathbb{R}^n$ and $\omega \in \mathbb{R}^n$, viewed as a linear functional

$\text{face}_{\omega}= \{ u \in P : \omega\cdot u \geq \omega\cdot v\mbox{ for all }v \in P \}$.

How does this definition match with general notion of the face of a polyhedron?

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    *at least one of (only one, if the polyhedron is convex).2012-03-04

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