1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Application of Burnside's Theorem, Colorings

  1. Apr 28, 2008 #1
    1. The problem statement, all variables and given/known data
    I have multiple problems, all dealing with Burnside's Theorem, perhaps help on one would help explain the others. How many ways may the faces of a cube be colored using 3 colors, up to symmetry of the cube. And, how many ways may the faces of a dodecahedron be colored using 5 colors up to symmetry.

    2. Relevant equations

    Burnside's Theorem: # colorings= 1/(group of symmetry)*Sum of number of fixed colorings

    3. The attempt at a solution

    The symmetry groups are S4 and A5 respectively. The part that I get hung up on is the number of fixed colorings. I know for the identity permutation on the cube, all colorings are fixed, but I don't know how the other rotations work. Please help!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted