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# Facet (mathematics)

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 Title: Facet (mathematics) Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Facet (mathematics)

For other uses of facet, see Facet (disambiguation)

In geometry, a facet is any of several things closely related to that of a face of a polyhedron or polytope, and in general refers to certain features of a shape that have dimension as large as possible.

• In three-dimensional geometry a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and need not be a face. For example, the faces of the convex hull of a non-convex polyhedron are facets of this polyhedron. To facet a polyhedron is to find and join such facets to form a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher dimensional polytopes.[1]
• In polyhedral combinatorics and in the general theory of polytopes, a facet of a polytope of dimension n is a face that has dimension n − 1. Facets may also be called (n − 1)-faces. In three-dimensional geometry, they are often called "faces" without qualification.[2]
• A facet of a simplicial complex is a maximal simplex, that is a simplex that is not a face of another simplex of the complex.[3] For simplicial polytopes this coincides with the meaning from polyhedral combinatorics.