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# Group Theory: Tetrahedron generators Watch

1. How would I start this question? Thank you for your time
2. The regular tetrahedron with 4 corners is a pyramid (with triangular base).

Once you can imagine this shape, look at all the possible rotations you can perform which leave the object looking the same after they are applied. Then consider how you could form a group from these rotations, i.e. which ones are generators, in terms of which points they exchange.
3. (Original post by gardash)

How would I start this question? Thank you for your time
You've been essentially told to use the Orbit/Stabiliser Theorem, so the first thing you should do is to find the size of the group you're looking for. Then when you've got a list of elements you know are in the group, you can use the useful fact that orbits partition the set, to ensure that you've not missed any rotations.
4. Just consider the cycle type of elements in the symmetric group corresponding to rotations then it will be easy to list them and also to justify your answer.

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Updated: May 14, 2013
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