Question

Answer the following questions to determine why Euler’s
formula continues to hold for the polyhedron formed by
cutting corners off of an octahedron, :
a. For an octahedron V = , ____,F = ____, and E =
_____.
b. When you slice off one corner of the octahedron,
you (gain or lose) ____ vertices, (gain or lose) ____
faces, and (gain or lose) ____ edges.
c. Therefore, the total change in V is ____; the total
change in F is ____; and the total change in V + F is
____.
d. The total change in E is ____.
e. What does the comparison of the total change in V + F
to the total change in E tell you?

Answer 1

In case you are not already familiar with the notations,
V=number of vertices (corners) of the octahedron.
F=number of faces
E=number of edges

The following link shows what happens when a corner of the octahedron is cut away. I'll let you complete the answers to the question.

http://img204.imageshack.us/img204/5302/euler.jpg