Thurs Jan Feb 10

 * go over homework:
     - solid cube group in detail (see solid_cube.txt)

 ** permutation cycles
    - group operation of successive permutations
    - practice
    - cycles
    - what "generates" the permutations?
       * transpositions
       * 3-cycles

 ** conjugate pairs,   U = F R F'
    - a notion of "same kind of thing"
    - conjugate => same cycle length
                   and 'same general properties'

 ** permutation puzzles in general:
    - Cayley graph (generator as "lines" leading out from solved to new positions)
    - each position is group element of transformation from solved to that position.
    - decomposition of each position into permutation cycles

 ** discuss how to start thinking about "solving" a permutation puzzle
    - operators

 ** Rubik's Cube as a permutation puzzle
    - corners
    - edges
    - faces

 ** counting positions