Posted by **jeng** on Saturday, October 24, 2009 at 1:00am.

Answer the following questions to determine why Euler’s

formula continues to hold for the polyhedron formed by

cutting corners off of an octahedron, as in Figure 11.35(b):

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?

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