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.