vertexen

Vertexen is the plural form of vertex, a term used in mathematics to denote a point where two or more edges meet, or a point in a graph where edges are incident. The concept appears across geometry, graph theory, and computer graphics, with related notions such as corners, nodes, and points in space.

In geometry, a vertex of a polygon is a corner where two edges meet and where the interior angle is defined. In polyhedra, a vertex is a point where three or more faces intersect. Vertices are typically described by coordinates in a chosen space and contribute to the shape's structure.

In graph theory, a vertex (also called a node) is a fundamental unit of a graph, connected by edges. The degree of a vertex is the number of incident edges. The handshaking lemma states that the sum of degrees over all vertices equals twice the number of edges (sum deg(v) = 2|E|).

In convex polyhedra, Euler's formula relates the numbers of vertices V, edges E, and faces F: V − E + F = 2. This relation constrains possible shapes and is a foundational result in topology.

In computer graphics, vertex data describes a point in 3D space and may include attributes such as position, normal, color, and texture coordinates. Vertex shaders compute per-vertex transformations and pass data to subsequent rendering stages.

Examples: a square has four vertices; a cube has eight; a tetrahedron has four.

Terminology: in Dutch contexts the plural vertexen is common; in English, the plural is vertices. The singular is vertex.