(Redirected from Facet (mathematics))Jump to navigation Jump to search
- In three-dimensional geometry a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face. To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes.
- 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.
- 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. For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics.
- Bridge, N.J. Facetting the dodecahedron, Acta crystallographica A30 (1974), pp. 548–552.
- Inchbald, G. Facetting diagrams, The mathematical gazette, 90 (2006), pp. 253–261.
- Coxeter, H. S. M. (1973), Regular Polytopes, Dover, p. 95.
- Matoušek, Jiří (2002), Lectures in Discrete Geometry, Graduate Texts in Mathematics, 212, Springer, 5.3 Faces of a Convex Polytope, p. 86.
- 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.
| 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 polyhedron-related article is a stub. You can help Wikipedia by expanding it.|