What does vertices mean?
Vertices are the points where the sides or edges of a geometric figure meet. A triangle has three vertices, while a quadrilateral has four; in three dimensions, the faces of a polyhedron meet at its vertices. The word also has an important technical use in graph theory, where a vertex represents a node and edges show connections between vertices. More generally, “vertices” can refer to prominent uppermost points, though this use is less common. The plural is especially natural in descriptions of geometry because many figures contain several such points. In everyday discussion, people may simply say “corners,” but vertices is the precise mathematical term. Its singular form is vertex, and the Latin ancestry of the word connects its geometric meaning with ideas of turning and direction.
nounVertices are the corner points of a polygon or polyhedron, or more generally the points at which lines, edges, or other boundaries meet. In graph theory, they are the individual nodes joined by edges.
- The corner or intersection points of a polygon, polyhedron, angle, or other geometric figure.
- The individual nodes at which edges meet in a graph or network.
- The highest or most prominent points of a shape, structure, or curve.
"The three vertices of the triangle were joined by a single blue line."
"Each face of the solid is bounded by four vertices."
"The algorithm assigns labels to the vertices before testing the graph for cycles."
Vertices is the standard plural of the singular noun vertex; vertexes is also encountered but is much less common.
"The vertices of the polygon are marked with small squares."
Vertices are the turning points of shapes—and “vertex” literally meant “turning point” in Latin.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of vertices
Vertices is the plural of the English noun vertex, borrowed from Latin vertex, meaning “highest point” or “turning point.” Latin vertex derives from vertere, “to turn,” and the related English words vertical, version, versatile, and convert share this root. The geometric sense developed through the word's original association with turning points and the highest points of forms.
Related word forms
How vertices is actually used
Vertices is the standard plural of vertex and is especially common in mathematics, geometry, and graph theory. It is a technical term but is readily understood outside those fields when describing corners or meeting points.
Easily confused with vertices
A vertex is any corner or intersection point of a geometric figure, whereas an apex specifically denotes the highest point or tip.