What is the shortest distance between two opposite points (two vertices separated by 2R) in the surface of a regular icosahedron? The regular icosahedron's edges are 1ft in length.
(In reply to
re(2): Solution (details) by Charlie)
Interesting...yes, your interpretation of the problem is probably what he intended. But then I think it could have been stated more clearly.
I am not familiar with spherical geometry, but assuming the law of cosines is as you state, your answer looks good to me. It also "feels" like it is about the right value for the dimensions given.
Too bad -- I kind of like the "distance in the surface" interpretation. It could be very hard to do if done differently than my approach.
re(3): Solution (details)
