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I have a student who is using Euler's formula to determine the number of panels a builder will need to construct a polyhedral dome that is made out of 40 steel pipes and 25 connecting joints. He explains to me that he is thinking the steel pipes are the faces and the connection joints are vertices. He concludes that the number of panels the builder needs equals 40+25=63. Is his reasoning correct? What follow-up question could I ask to make certain he understands the use of Euler's formula?
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