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]
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.
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