Edge (geometry)

Three edges AB, BC, and CA, each between two vertices of a triangle.
A polygon is bounded by edges; this square has 4 edges.
Every edge is shared by two faces in a polyhedron, like this cube.
Every edge is shared by three or more faces in a 4-polytope, as seen in this projection of a tesseract.

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.^[1] In a polygon, an edge is a line segment on the boundary,^[2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet.^[3] A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.

An edge may also be an infinite line separating two half-planes.^[4] The sides of a plane angle are semi-infinite half-lines (or rays).^[5]

^ Ziegler, Günter M. (1995), Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152, Springer, Definition 2.1, p. 51, ISBN 9780387943657.
^ Weisstein, Eric W. "Polygon Edge". From Wolfram MathWorld.
^ Weisstein, Eric W. "Polytope Edge". From Wolfram MathWorld.
^ Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 64, ISBN 0-07-072191-2
^ Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 68, ISBN 0-07-072191-2

[1] Ziegler, Günter M. (1995), Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152, Springer, Definition 2.1, p. 51, ISBN 9780387943657.

[2] Weisstein, Eric W. "Polygon Edge". From Wolfram MathWorld.

[3] Weisstein, Eric W. "Polytope Edge". From Wolfram MathWorld.

[4] Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 64, ISBN 0-07-072191-2

[5] Wylie Jr., C.R. (1964), Foundations of Geometry, New York: McGraw-Hill, p. 68, ISBN 0-07-072191-2

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