1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Permutations in rotations and reflections

  1. Feb 18, 2010 #1
    Hi all, I've been having difficulty with the following question.

    Let P be a regular pentagon. Let R be the rotation of P by 72degrees anticlockwise and let F be the reflection of P in the vertical line of symmetry. Represent R and F by permutations and hence calculate: F R^2 F R F^3 R^3 F, expressing this first as a permutation and then as a symmetry of P.


    I think I've correctly worked out R as the cycle (15432) and F = (25)(34). I've written these as permutations however, I don't understand how to do the calculation asked for and what it means by 'expressing as a symmetry of P'.

    Any ideas would be much appreciated. Thanks in advance!
     
  2. jcsd
  3. Feb 18, 2010 #2
    The calculation is just the composition of the R and F permutations, in the specified order. In your case, you first rotate counterclockwise by 72 degrees (F), then reflect three times (here, you may use the fact that R2=I, where I is the identity), then rotate again by 3x72 degrees, etc.

    The final expression should express a symmetry.
     
  4. Feb 18, 2010 #3

    So, I should work out the permutations for F, R^2, ... etc. and then multiply them all in the order stated. Is this what you're saying? (Sorry I didn't quite understand).
     
  5. Feb 18, 2010 #4
    Yes, that's pretty much it.
     
  6. Feb 18, 2010 #5
    Ok, thank you. =)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook