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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
*In three-dimensional geometry a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face.〔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.〕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 simplicial polytopes this coincides with the meaning from polyhedral combinatorics.
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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