# Polyhedron

(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.