A polyhedron can be defined as the intersection of a finite number of linear equalities and inequalities. They can be represented as \(\{ x \mid Ax \prec b, Cx = d \}\). Since polyhedrons are intersections of [Hyperplane]s and [Halfspace]s and since we know that they are [Convex Set]s and convex sets are closed under intersections, we can conclude that polyhedrons are also convex sets.