Edge (geometry)

An edge between two vertices	A polygon is bounded by edges, like this square has 4 edges.
Every edge shares two faces in a polyhedron, like this cube.	Every edge shares three or more faces in a 4-polytope, as seen in this projection of a tesseract.

For edge in graph theory, see Edge (graph theory).

In geometry, an edge is a line segment joining two adjacent vertices in a polygon. Thus applied, an edge is a connector for a one-dimensional line segment and two zero-dimensional objects.

A planar closed sequence of edges forms a polygon (and a face). In a polyhedron, exactly two faces meet at every edge, while in higher dimensional polytopes, three or more faces meet at an edge.

In a polygon, an edge can also be called a facet or side, bounding the polygon. In a polyhedron, an edge can also be considered a ridge, being the shared boundary between two faces, and in a 4-polytope, an edge can be considered a peak, with a cycle of 3 or more faces and cells wrapping around it.

See also

• Euler characteristic

External links

• Olshevsky, George, Edge at Glossary for Hyperspace.
• Weisstein, Eric W., "Polygonal edge" from MathWorld.
• Weisstein, Eric W., "Polyhedral edge" from MathWorld.