Vertex (geometry)

: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect.

As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

[3][4] A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.

[5] More generally, a vertex of a polyhedron or polytope is convex, if the intersection of the polyhedron or polytope with a sufficiently small sphere centered at the vertex is convex, and is concave otherwise.

There is also a connection between geometric vertices and the vertices of a curve, its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated by a smooth curve, there will be a point of extreme curvature near each polygon vertex.