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.

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