Facet (geometry)

From Wikipedia, the free encyclopedia
For other uses of facet, see Facet (disambiguation)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

  • 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.[citation needed] 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.

References

  1. ↑ Coxeter, H. S. M. (1973), Regular Polytopes, Dover, p. 95 .
  2. ↑ Matoušek, Jiří (2002), Lectures in Discrete Geometry, Graduate Texts in Mathematics 212, Springer, 5.3 Faces of a Convex Polytope, p. 86 .
  3. ↑ De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco (2010), Triangulations: Structures for Algorithms and Applications, Algorithms and Computation in Mathematics 25, Springer, p. 493, ISBN 9783642129711 .

External links

Disambiguation icon This article includes a list of related items that share the same name (or similar names).
If an internal link incorrectly led you here, you may wish to change the link to point directly to the intended article.
This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.