geometry

posted by jeng

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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