Vertices, Edges and Faces

Vertex, Edge and Face
A vertex is a corner.
An edge is a line segment between faces.
A face is a single flat surface

Let us look more closely at each of those:



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

It is a Corner.

This tetrahedron has 4 vertices.

And this pentagon has 5 vertices:   Pentagon vertices  


Pentagon edges
This Pentagon
Has 5 Edges


For a polygon an edge is a line segment on the boundary joining one vertex (corner point) to another.

This Tetrahedron
Has 6 Edges


For a polyhedron an edge is a line segment where two faces meet.



A face is any of the individual flat surfaces of a solid object.

This tetrahedron has 4 faces (there is one face you can't see)



"Side" is not a very accurate word, because it can mean:


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.)


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