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:



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 on the boundary or where faces meet.



For a polyhedron they are where two faces meet.

This tetrahedron has 6 edges.


For a polygon they are on the boundary.
Sometimes called sides.

This pentagon has 5 edges:

  Pentagon edges



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


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.)