Vertices, Edges and Faces

Vertex, Edge and Face
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

Vertex

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

It is a Corner.

This tetrahedron has 4 vertices.

And this pentagon has 5 vertices:   Pentagon vertices  

Edges

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

Edges

 

... where two faces meet on a polyhedron

(this tetrahedron has 6 edges),

 

... or on the boundary of a polygon

(this pentagon has 5 edges)

  Pentagon edges

A polygon's edges are sometimes called sides.

Faces

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

always equals 2

This can be written: F + V − E = 2

cube

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.)