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Facet (mathematics)

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Title: Facet (mathematics)  
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Subject: Polytope, Triangle inequality, Ceva's theorem, List of regular polytopes, Convex polytope, Rectification (geometry), Louis Guttman, Coxeter–Dynkin diagram, Expansion (geometry), Linear programming relaxation
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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.


External links

  • MathWorld.
  • Facet at Glossary for Hyperspace.

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