Vertices, Edges and Faces

Vertex, Edge and Face
A vertex is a corner.
An edge joins one vertex with another.
A face is an individual surface

Let us look more closely at each of those:



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  



An edge is a line segment that joins two vertices.

This tetrahedron has 6 edges.

And this pentagon has 5 edges:

  Pentagon edges

An edge can also be the boundary of a shape.

Such as the circumference of a circle.



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,


6 + 8 − 12 = 2

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