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I am am work on my mathematics extended essay, and I want to do it on:

1. Coming up with a general formula for the volume of the five Platonic Solids (I need to know from other mathematics higher level students if this is two simple).

2. The proof(s) for Euler's polyhedron formula.

3. The Travelling Salesman Problem (not sure how much math is involved as opposed to computer science).

I am most interested in the first but willing to drop it if it is too simple. I am also open to suggestions of other interesting topics in geometry (the subject I have the most interest in).
I want to get some work done before the summer break ends in about 4 weeks, so I could really use some advice (especially considering my adviser has gone incognito).

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