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A face of a convex set, not equal to the set, of maximal dimension. If the set is polyhedral, say LaTeX: P = \{x: Ax \le b\}, where the defining inequalities are irredundant, then the facets are in one-to-one correspondence with LaTeX: \{x \in P: A_{i,:} x = b_i\} for LaTeX: i such that the equality is not forced – i.e., there exists LaTeX: x in LaTeX: P for which LaTeX: A_{i,:} x < b_i. Here LaTeX: A_{i,:} is the i-th row of LaTeX: A.

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