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EspañolFACET (MATHEMATICS)
:''For other uses, see facet (disambiguation).''
In the general theory of polyhedra and polytopes, two conflicting meanings are currently jostling for acceptability:
★ A 'facet' of a geometric polyhedron is traditionally any polygon whose corners are vertices of the polyhedron. By extension to higher dimensions, it is any ''j''-tope (''j''-dimensional polytope) whose vertices are shared by some ''n''-tope (''n''-dimensional polytope where 0<''j''<''n''). To 'facet' a polytope is to find and join such facets to form a new polytope - this process is called 'facetting' or 'faceting' and is the reciprocal process to stellation.
★ A 'facet' of an ''n-polytope'' is, more recently, an (''n''-1)-dimensional face or '(''n''-1)-face'.
★ :For example:
★ :#The facets of a polygon are edges. (1-faces)
★ :#The facets of a polyhedron are faces. (2-faces)
★ :#The facets of a polychoron (4-polytope) are cells. (3-faces)
★ :#The facets of a polyteron (5-polytope) are hypercells. (4-faces)
★ :Exactly two facets meet at any ridge in a polytope. By extension, 'facet' or '''j''-facet' is sometimes used to mean any ''j''-dimensional element of a polytope.
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In the general theory of polyhedra and polytopes, two conflicting meanings are currently jostling for acceptability:
★ A 'facet' of a geometric polyhedron is traditionally any polygon whose corners are vertices of the polyhedron. By extension to higher dimensions, it is any ''j''-tope (''j''-dimensional polytope) whose vertices are shared by some ''n''-tope (''n''-dimensional polytope where 0<''j''<''n''). To 'facet' a polytope is to find and join such facets to form a new polytope - this process is called 'facetting' or 'faceting' and is the reciprocal process to stellation.
★ A 'facet' of an ''n-polytope'' is, more recently, an (''n''-1)-dimensional face or '(''n''-1)-face'.
★ :For example:
★ :#The facets of a polygon are edges. (1-faces)
★ :#The facets of a polyhedron are faces. (2-faces)
★ :#The facets of a polychoron (4-polytope) are cells. (3-faces)
★ :#The facets of a polyteron (5-polytope) are hypercells. (4-faces)
★ :Exactly two facets meet at any ridge in a polytope. By extension, 'facet' or '''j''-facet' is sometimes used to mean any ''j''-dimensional element of a polytope.
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psst.. try this: add to faves
