Editing Polyhedron (section)

== Higher-dimensional polyhedra ==
{{Main|n-dimensional polyhedron}}
From the latter half of the twentieth century, various mathematical constructs have been found to have properties also present in traditional polyhedra. Rather than confining the term "polyhedron" to describe a three-dimensional polytope, it has been adopted to describe various related but distinct kinds of structure.

A polyhedron has been defined as a set of points in [[real number|real]] [[affine space|affine]] (or [[Euclidean space|Euclidean]]) space of any dimension ''n'' that has flat sides.  It may alternatively be defined as the intersection of finitely many [[half-space (geometry)|half-spaces]].  Unlike a conventional polyhedron, it may be bounded or unbounded. In this meaning, a [[polytope]] is a bounded polyhedron.<ref name="polytope-bounded-1" /><ref name="polytope-bounded-2" />

Analytically, such a convex polyhedron is expressed as the solution set for a system of linear inequalities. Defining polyhedra in this way provides a geometric perspective for problems in [[linear programming]].<ref name=":0">{{Cite Geometric Algorithms and Combinatorial Optimization}}</ref>{{Rp|page=9}}