Generally, a face is a component polygon, polyhedron, or polytope. A two-dimensional face thus has vertices and edges, and can be used to make cells. More formally, a face is the intersection of an n-dimensional polytope with a tangent hyperplane. Zero-dimensional faces are known as polyhedron vertices (nodes), one-dimensional faces as polyhedron edges, (n-2)-D faces as ridges, and (n-1)-dimensional faces as facets.


The illustration above illustrates the most commonly encountered face, namely that of a three-dimensional polyhedron.

See also

Face Diagonal, Facet, Polyhedron Edge, Polyhedron Vertex, Polytope, Ridge

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Cite this as:

Weisstein, Eric W. "Face." From MathWorld--A Wolfram Web Resource.

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