Facet (mathematics)
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For other meanings, 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). The process of finding and joining such facets to form a new polytope is called facetting 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. Exactly two facets meet at any ridge in a polytope.
