- Facet (mathematics)
A facet of a

simplicial complex is a maximal simplex.In the general theory of

polyhedra andpolytope s, two conflicting meanings are currently jostling for acceptability:*A

**facet**of a geometricpolyhedron is traditionally any polygon whose corners are vertices of the polyhedron. By extension to higher dimensions, it is any "j"-tope ("j"-dimensionalpolytope ) 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 calledorfacetting **faceting**and is the reciprocal process tostellation .

*A**facet**of an "n-polytope " is, more recently, an ("n"-1)-dimensional face or**("n"-1)-face**. The informal term**side**can mean the same thing, edges of a polygon and faces of a polyhedron.

*:For example:

*:#The facets of a polygon are edges. (1-faces)

*:#The facets of apolyhedron or tiling are faces. (2-faces)

*:#The facets of apolychoron (4-polytope) or honeycomb are cells. (3-faces)

*:#The facets of apolyteron (5-polytope) or 4-honeycomb arehypercell s. (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.**External links***

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*Wikimedia Foundation.
2010.*

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