Edge (geometry)

Not to be confused with Edge (graph theory).

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. In a polygon, an edge is a line segment on the boundary, 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. 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. The sides of a plane angle are semi-infinite half-lines (or rays).

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