Activity III.C

Build a model of the seventy-atom fullerene in which there are no contiguous pentagons. A model of C can be constructed from the C model by separating C in halves and then inserting a ring of ten additional atoms. The result is a football-shaped molecule. Consider the following questions while inspecting your model.

1. How many five- and six-membered rings are there in C?
   Answer: twelve 5's and twenty-five 6's.

2. How many different kinds of vertices are there?
   Answer: five.

3. How many of each kind of vertex are there?
   Answer: The five kinds of vertices are present in a ratio of 10:10:20:20:10.

4. How many edges are there?
   Answer: 105.

5. How many different kinds of edges are there?
   Answer: eight. There are four types of 6-6 ring fusions and four types of 6-5 ring fusions.

6. How many 6-6 ring fusions and 6-5 ring fusions are there?
   Answer: 45 of the 6-6 variety and 60 of the 6-5 type.

7. Given that the average edge is approximately 1.4 Å long, estimate the size of the cavity (length and width).
   Answer: Length is ~ 7.6 Å and width is ~ 6.4 Å.

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