# Vertices, Edges and Faces

A vertex is a corner.
An edge is a line segment that joins two vertices.
A face is an individual surface
.

Let us look more closely at each of those:

## Vertices

A vertex (plural: vertices) is a point where two or more lines meet.

It is a Corner.

This tetrahedron has 4 vertices.

 And this pentagon has 5 vertices:

## Edges

An edge is a line segment that join two vertices ...

... where two faces meet on a polyhedron

(this tetrahedron has 6 edges),

 ... or on the boundary of a polygon (this pentagon has 5 edges)

A polygon's edges are sometimes called sides.

## Faces

 A face is any of the individual surfaces of a solid object. This tetrahedron has 4 faces (there is one face you can't see)

## Euler's Formula

For many solid shapes the

• Number of Faces
• plus the Number of Vertices
• minus the Number of Edges

always equals 2

This can be written: F + V − E = 2

 Try it on the cube: A cube has 6 Faces, 8 Vertices, and 12 Edges, so: 6 + 8 − 12 = 2 (To find out more about this read Euler's Formula.)