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Undid revision 1024715813 by Fgnievinski (talk) do you always universally repeat duplicate word synonyms? "Planar surface" already is sufficient; we don't have to call it a planar surface region area patch. |
Fgnievinski (talk | contribs) Undid revision 1024724893 by David Eppstein (talk) you'd have to redefine plane (geometry): "a flat, two-dimensional surface that extends *infinitely* far." |
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In [[solid geometry]], a '''face''' is a flat ([[Plane (geometry)|planar]]) surface [[region (mathematics)|region]] that forms part of the boundary of a [[solid object]];<ref>{{cite book | title = [[Merriam-Webster's Collegiate Dictionary]] | edition = Eleventh | publisher = [[Merriam-Webster]] | location = Springfield, MA | year = 2004}}</ref> a three-dimensional solid bounded exclusively by faces is a [[polyhedron]].
In more technical treatments of the geometry of polyhedra and higher-dimensional [[polytope]]s, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions).<ref name="m">{{citation|title=Lectures in Discrete Geometry|url=https://books.google.com/books?id=0N5RVe5lKQUC&pg=PA86|at=5.3 Faces of a Convex Polytope, p. 86|volume=212|series=[[Graduate Texts in Mathematics]]|publisher=Springer|year=2002|author-link=Jiří Matoušek (mathematician)|first=Jiří|last=Matoušek|isbn = 9780387953748}}.</ref>
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