 # Vertices, Faces And Edges

In this article, we will discuss the vertices, faces, and edges of solid shapes. We come across a number of objects of different shapes and sizes in our day to day life. There are golf balls, door mats, ice-cream cones, coke cans and so on. These objects have different characteristic properties such as length, breadth, diameter, etc. which set them apart from one another. But no matter how different their dimensions are, all of them occupy space and have three dimensions. So they are referred to as three-dimensional or solid shapes. And there are figures that can be represented on a plane (as a piece of paper). They have 2 dimensions, length, and breadth. And they are referred to as two-dimensional or plane figures.

## Vertices

A vertex meaning in maths defined as a point where two or more edges meet. These are the corner points. • Cubes and cuboids have 8 vertices.
• Cones have 1 vertex.
• Cylinders have no vertex.
• Spheres have no vertex (the surface is a curve).

## Faces

Every individual flat surface of a solid is called its face. Solids have more than one face. • Cubes and cuboids have 6 faces.
• Cones have a flat face and a curved face.
• Cylinders have 2 flat faces and a curved face.
• A sphere has a curved face.

## Edges

The line segment which acts as an interface between two faces is called an edge. Sometimes it is also described as the line segment joining two vertices. • Cubes and cuboids have 12 edges.
• Cones have 1 edge.
• Cylinders have 2 edges.
• Sphere has no edge.

### Relation Between Vertices, Faces and Edges

The relation between vertices, faces and edges can be easily determined with the help of Euler’s Formula. Having learned about the faces, edges, and vertices of solids, let us note an interesting relationship between the three of them. It is to be kept in mind that the formula holds good for closed solids which have flat faces and straight edges such as the cuboids. It cannot be used for cylinders because they have curved edges.

Euler’s formula is given by

F + V – E = 2

where F, V, and E are the number of faces, vertices, and edges of the polyhedra respectively.