vertexes

Vertexes, or vertexes, is the plural form of vertex. The singular is vertex. The term is used across geometry, graph theory, and computer graphics, though vertices is the more common plural in modern mathematical usage. The word derives from Latin vertex, meaning apex or turning point.

In geometry, a vertex of a polygon is a corner where two sides meet, forming the polygon’s interior angle. In polyhedra, a vertex is a point where three or more edges meet; the arrangement of vertices and edges defines the solid’s shape and topology. For convex polyhedra, the relationship among counts of faces (F), edges (E), and vertices (V) is captured by Euler’s formula: F − E + V = 2.

In graph theory, a vertex (also called a node) is a fundamental unit of a graph, with edges connecting pairs of vertices. The degree of a vertex is the number of incident edges. In a finite graph, the sum of the degrees of all vertices equals twice the number of edges, a relation that underpins many combinatorial arguments.

In computer graphics and geometric modeling, a vertex represents a point in space, typically defined by coordinates and optional attributes such as normals, texture coordinates, or color. Vertex data are stored in buffers and processed by shaders during rendering, making vertices a central concept in the construction and visualization of geometric shapes.