Euler's Formula

 This classic formula holds for any convex polyhedron. The number of vertices and faces together is exactly two more than the number of edges.  Symbolically V-E+F=2, where V is the number of vertices, E is the number of edges, and F is the number of faces of the polyhedron. 
Portrait of Euler

Example 1)
Notice that the Polyhrdron to the left has 5 vertices, 8 edges, and 5 faces.  By Euler's formula, we set up:  5-8+5=2

Now you try one:

Choose the number of faces, vertices, and edges.  Then check to see if Euler's formula holds for this polyhedron.

Try another: