**Vertices are the points, or corners, in geometrical and mathematical shapes where two or more lines meet but do not cross, according to Math Open Reference.** Vertices can exist in two-dimensional and three-dimensional shapes. The singular form of vertices is vertex. Sometimes, the term vertex is also used to describe certain points on quadratic equations.

Vertices are often used as a description of the corner of a shape, generally a polygon. However, they can also exist at a point between any two lines which meet and form an angle but do not cross. If the lines cross, the point is considered an intersection and not a vertex. Vertices are a useful way to describe objects and their placement in two-dimensional and three-dimensional spaces. Two-dimensional objects have vertices where their lines meet, and three-dimensional objects have vertices where their planes meet. In this sense, vertices can sometimes be described as the corners of a geometric structure.

In mathematics, the term vertex can also refer to the peak of a parabola. A parabola is a curved shape that is generated by graphically representing a quadratic equation. The peak of a parabola is either the highest or lowest point on the curve, depending on whether it opens upwards or downwards.