Every polyhedral cone can be described in two different ways : with inequalities or conic combinations.
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Polyhedral cones play a central role in the representation theory of bounded polyhedron is a polytope.
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Every finitely generated cone is a polyhedral cone, and every polyhedral cone is a finitely generated cone.
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Every finitely generated cone is a polyhedral cone, and every polyhedral cone is a finitely generated cone.
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In the inequality description, the polyhedral cone C can be given by a matrix A such that C = \ { x \ in \ mathbb { R } ^ n \ mid Ax \ geq 0 \ }.
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In the non-degenerate cases this convex set is a convex polyhedron ( possibly unbounded, e . g ., a half-space, a slab between two parallel half-spaces or a polyhedral cone ).
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A strongly convex rational polyhedral cone in " N " is a convex cone ( of the real vector space of " N " ) with apex at the origin, generated by a finite number of vectors of " N ", that contains no line through the origin.
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