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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.
- 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 simplicial polytopes this coincides with the meaning from polyhedral combinatorics.
- 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.
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