Any geometric figure, shape or form is made up of various vertices, edges or lines, faces and spans an area. Vertices, the plural of vertex, are points where two or more straight lines converge and meet. One could also say that a vertex is the point wherefrom two or more straight lines diverge or originate.
Imagine a triangle. It has three straight lines converging at specific angles. You would see that there are three sharp points of a triangle. All these three sharp points where two straight lines meet are called vertices. In case of an equilateral triangle where all the three sides or straight lines are of the same length and the three angles formed inside the triangle are sixty degrees each, the three vertices are identical. The shape and form of the vertices would change as the length of the straight lines change, also changing the resulting angles.
2D and 3D Vertices
Geometric shapes or forms exist in two dimensions and three dimensions. A two dimensional figure like the triangle has three vertices, a square or a rectangle would have four vertices, a pentagon would have five and a hexagon would have six. Likewise, a heptagon and octagon would have seven and eight vertices respectively. In case of three dimensional figures, a cube would have eight vertices, a tetrahedron has four vertices, a pyramid would have five vertices and a triangular prism would have six vertices. A cone which is one of the simplest three dimensional illustrations of a triangle has only one vertex. In case of two dimensional forms, only two lines meet at a vertex. In three dimensional figures or shapes, more than two lines meet at every vertex.
It must be noted that spherical forms don’t have any vertex. A circle or a sphere, which is the three-dimensional form of a circle, doesn’t have any vertex. A cylinder doesn’t have any vertex.
Vertices are not only considered as the converging or diverging points of straight lines or edges of a shape, form or figure. They are also responsible in forming the angles depending on how the straight lines converge or diverge and meet. In case of squares and rectangles or cubes, the angles formed are right angles or ninety degrees. In case of triangles and other polygons, the angles would depend on the size of the edges and the exact shape or form of the figure.