Polyhedron

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(pl. polyhedra). A set that equals the intersection of a finite number of halfspaces. This is generally written as LaTeX: \textstyle \left \{x: Ax \le b \right \}, where the representation LaTeX: (A,b) is not unique. It is often useful to separate the implied equalities: LaTeX: \textstyle \left \{x: Ax \le b, Ex = c \right \}, so that the relative interior is LaTeX: \textstyle \left \{x: Ax < b, Ex = c \right \}. The system, LaTeX: \textstyle \left \{Ax \le b, Ex = c \right \}, is a prime representation if it is irredundant, and it is minimal if it is irredundant and contains no implied equality. A polyhedron is degenerate if it contains an extreme point that is the intersection of more than LaTeX: n halfspaces (where LaTeX: n is the dimension of the polyhedron). An example is the pyramid.


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