# 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 = (To find out more about this read Euler's Formula.) |