Reflecting The Last Layer


Reflecting the last layer can be done in one of two ways:
  1) Over the x axis
  2) Over the y axis

 This graphic shows how the x and y axes 
 are laid out on the last layer.

 This graphic is symmetric about the x axis.

 This graphic is symmetric about the y axis.

 On the x axis reflection, the B and F faces 
 are the only two faces that reflect off of
 themselves.  This means that F reflects to
 B', F' to B, B to F', and B' to F.  All
 other faces become their own opposites.
 This means R reflects to R' and so on.

 On the y axis reflection, the R and L faces 
 are the only two faces that reflect off of
 themselves.  This means that R reflects to
 L', R' to L, L to R', and L' to R.  All
 other faces become their own opposites.
 This means U reflects to U' and so on.

Example of reflecting an orientation pattern:

From Table Over x-axis Over y-axis
L' B L U L' B' L B U' B' L F' L' U' L F L' F' U F R B' R' U' R B R' B' U B


Example of reflecting a permutation pattern:

From Table Over x-axis Over y-axis
B'U R'F R B R'F'R U B'U² B U F U'R B'R'F'R B R'U'F U² F'U' B U'L F'L'B'L F L'U'B U² B'U'

Note that it does not matter which reflection is chosen because they are identical. If you reflect over the x-axis and then turn the cube in your hand so that the back face becomes the front face (180 degree turn of the entire cube), you will have the same thing as if you had reflected over the y-axis.

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