KNOWPIA
WELCOME TO KNOWPIA

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

- In three-dimensional geometry, a
**facet of a polyhedron**is any polygon whose corners are vertices of the polyhedron, and is not a*face*.^{[1]}^{[2]}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.^{[3]} - In polyhedral combinatorics and in the general theory of polytopes, a face that has dimension
*n*− 1 (an (*n*− 1)-face or hyperface) is also called a**facet**.^{[4]} - 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.^{[5]}For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics.

**^**Bridge, N.J. (1974). "Facetting the dodecahedron".*Acta Crystallographica*.**A30**(4): 548–552. doi:10.1107/S0567739474001306.**^**Inchbald, G. (2006). "Facetting diagrams".*The Mathematical Gazette*.**90**(518): 253–261. doi:10.1017/S0025557200179653. S2CID 233358800.**^**Coxeter, H. S. M. (1973), "6 Star-Polyjedra",*Regular Polytopes*, Dover, p. 95**^**Matoušek, Jiří (2002), "5.3 Faces of a Convex Polytope",*Lectures in Discrete Geometry*, Graduate Texts in Mathematics, vol. 212, Springer, p. 86, ISBN 9780387953748.**^**De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco (2010),*Triangulations: Structures for Algorithms and Applications*, Algorithms and Computation in Mathematics, vol. 25, Springer, p. 493, ISBN 9783642129711.

- Weisstein, Eric W. "Facet".
*MathWorld*.