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 -dimensional polytope with a tangent hyperplane. Zero-dimensional faces are known as polyhedron vertices (nodes), one-dimensional faces as polyhedron edges, -D faces as ridges, and -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 Resource. https://mathworld.wolfram.com/Face.html