Thurs Feb 3

 * isometries in S4, A4, C4, D4, S5, A5, C5, D5
 * properties of individual elements:
     - cycle length
     - commutator of something? (define "communtator")
       
 * discuss solid cube group (starting this was the homework assignment)
     1   Identity (cycle length = 1)
     6   F, R, U, F', R', U' (cycle length = 4; 90 degree face-centered rotation)
     3   F2, R2, U2  (cycle length = 2; 180 degree face-centered rotation)
     8   FR etc (cycle length = 3; 120 degree corner-centered rotation)
     6   RRU etc (cycle length = 2; 180 degree edge-centered rotation)
     --- 
         sum = 24

 * treat R,F,U,R',F',U' as generators; draw the graph for this 24 element group

 * Are R,F,U generators?  R,F?  R?  Any single element?

 * odd/even 

 * notation on rubik's cube; commutators; cycle length (assign)
     
 * time allowing : 
     matrix multiplication rules
     permutation matrices

 * for Thurs Feb 10 
     1.Find the commutator subgroup of the solid cube group. 
     2.Do R, F generate the cube group? R,F,U?  R??
     3.What is the cycle length of the Rubik's commutator FRF'R' ? FR ?


 - next time:
    * if c = a b a' then we say "c and b are conjugate".
    * conjugacy classes
    * conjugacy classes of solid cube