nonvertex

Nonvertex is a term used to describe any point or element that is not a vertex of a specified geometric or combinatorial object. The exact meaning of nonvertex depends on context, since which points count as vertices varies with the object under consideration.

In geometry, a nonvertex point of a polygon includes every point on its edges that is not a corner and every interior point. For a polyhedron or polytope, nonvertices are points on faces, along edges, or inside the solid that are not the vertices where edges meet. In meshes and triangulations, nonvertex points typically refer to points that are not chosen as mesh vertices, such as interior points of triangles or points on edges that are not endpoints.

In graph theory and related areas, the term is less standardized. Some discussions distinguish between vertices (the defined endpoints of edges) and all other points in the ambient space or the drawing, calling the latter nonvertices in a descriptive way. More precise language in formal work often substitutes phrases like interior point, edge point, or face point to avoid ambiguity.

Usage and interpretation are highly context-dependent, so readers should rely on the definitions provided in a given text. The concept of nonvertex serves to separate the designated vertex set from all other points within the same geometric or combinatorial setting.

See also: Vertex, Edge, Face, Interior point, Boundary, Mesh, Polytope, Graph.