Face (geometry)

In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object;^[1] a three-dimensional solid bounded exclusively by faces is a polyhedron. A face can be finite like a polygon or circle, or infinite like a half-plane or plane.^[2]

In more technical treatments of the geometry of polyhedra and higher-dimensional polytopes, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions).^[3]

^ Merriam-Webster's Collegiate Dictionary (Eleventh ed.). Springfield, MA: Merriam-Webster. 2004.
^ Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 66, ISBN 0-07-072191-2
^ Matoušek, Jiří (2002), Lectures in Discrete Geometry, Graduate Texts in Mathematics, vol. 212, Springer, 5.3 Faces of a Convex Polytope, p. 86, ISBN 9780387953748.

[1] Merriam-Webster's Collegiate Dictionary (Eleventh ed.). Springfield, MA: Merriam-Webster. 2004.

[2] Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 66, ISBN 0-07-072191-2

[m-3] Matoušek, Jiří (2002), Lectures in Discrete Geometry, Graduate Texts in Mathematics, vol. 212, Springer, 5.3 Faces of a Convex Polytope, p. 86, ISBN 9780387953748.

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