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Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.〔.〕 In a polygon, an edge is a line segment on the boundary,〔Weisstein, Eric W. "Polygon Edge." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolygonEdge.html〕 and is often called a side. (Thus a segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.) In a polyhedron or more generally a polytope, an edge is a line segment where two two-dimensional faces meet.〔Weisstein, Eric W. "Polytope Edge." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolytopeEdge.html〕
==Relation to edges in graphs==
In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which have a concrete geometric representation as a line segment.
However, any polyhedron can be represented by its skeleton or edge-skeleton, a graph whose vertices are the geometric vertices of the polyhedron and whose edges correspond to the geometric edges.〔.〕 Conversely, the graphs that are skeletons of three-dimensional polyhedra can be characterized by Steinitz's theorem as being exactly the 3-vertex-connected planar graphs.〔. See in particular Theorem 3, (p. 176 ).〕
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