Supporting hyperplane

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A supporting hyperplane is a concept in geometry. A hyperplane divides a space into two half-spaces. A hyperplane is said to support a set S if it meets both of the following:

• S is entirely contained in one of the two closed half-spaces of the hyperplane
• S has at least one point on the hyperplane

Here, a closed half-space is the half-space that includes the hyperplane.

[edit] Uses

• If the hyperplane H supports the polytope P, their intersection is said to be a face of P.