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.