## ::Edge (geometry)

### ::concepts

Edges::geometry Graph::vertices Faces::title Books::first Polygon::citation Polytope::convex

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.<ref>{{#invoke:citation/CS1|citation
|CitationClass=citation
}}.</ref> In a polygon, an edge is a line segment on the boundary,<ref>Weisstein, Eric W. "Polygon Edge." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolygonEdge.html</ref> 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.<ref>Weisstein, Eric W. "Polytope Edge." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolytopeEdge.html</ref>

**Edge (geometry) sections**

Intro Relation to edges in graphs Number of edges in a polyhedron Incidences with other faces Alternative terminology See also References External links

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