2x2x2 Cube Antipodes

I have written a GUI NxNxN cube program to which I just added a 2x2x2 cube auto solve function. To test the performance of the solution algorithm I wanted try it on the 14 q-turn antipodes. So I did the depth-wise expansion of the group, found the 276 antipodes and reduced them with M symmetry. In the context of the fixed DBL cubie 2x2x2 model, that is the <R U F> group model, M symmetry classes are formed by ( c * m' * q * m ) where q is a group element, m ranges over the cubic symmetry group and c is the whole cube rotation needed to place the conjugate back in the group.

For those who might be interested, here are the results of the symmetry reduction and turn sequences for representative elements of the antipode classes.

Class size:  4 Count:  1
Class size:  6 Count: 36
Class size:  8 Count:  1
Class size: 12 Count:  4
Class count: 42
 
 R R U R' U F U' F F R F' R F F
 R R U' R' U F U' R F R' F U' R F'
 R R U R' F R' F R F' U F F U' F
 R R U F R' U U F U' F' R U' R R
 R R U R U' F U' R R U' R' U' F' R
 R R U R F R' U R R U' F U' F' U'
 R R U' R' F' U R' U' R F' U' R' U R
 R R U R F' U U R F' R' F R' U U
 R R U R' U F U' R F R' U' R U R
 R R F R F' R U' R F' U U F R R
 R R U R' U' F' U U R F' U' F F U
 R R U R' U' F' U U F' U F R' F U
 R R F F R F' U R U U F' R U' R'
 R R F R F R' F U' R F' R F' R' F'
 R R U R' U' R R U F' R U F R' F
 R R U R U' F R' F' R F' U U F F
 R R U R R F U' R' U' R F' U F F
 R R U R R U F U' R F' U F U' F
 R R U R R F U' F' U' R F' R F F
 R R U R' U' R U' F' U U R U' R F
 R R U U F' R F R U F F R' F' U
 R R U F U' R F F R' U' R F' R U'
 R R F U R U' F U' R U' F U' R' U'
 R R U R' U F' R U F U' R' F' U F'
 R R F F R U' R U R R F' R U' F'
 R R U R U F' U F' U' F U' F R F
 R R U R' F U' R U F R' U' F' U F'
 R R F R U R' F U' F R' F R' F' R'
 R R U R' F' R R F R' F U R U' R
 R R U F R' U F F U' F' U F' R U'
 R R U U R U' R' F R R U R' U F'
 R R U U R F' U' F R R U F' R U'
 R R U' F R U F' U U F' U' R U' R
 R R U R' U U F U U F' R U' F U'
 R R U R' U' F' R U' F F R' F R' F
 R R U R' F' R' U R R U R F' U F'
 R R U R F' R F' R R U F' U' F' U'
 R R U R R U R F' U F' U F U' R
 R R U R' U' R F U' R' F' R U' R U'
 R R U' R' U R F' U R F' R' F R' U
 R R U F R' U' F U' R' F U R' U R'
 R R U F' R R F' R' F F U R' F' U

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2x2x2 Cube Antipodes

I am native german and maybe i am choosing the wrong words to explain what i mean, so please do not care about it.
There is a second thread about the antipodes of the pocket cube, but i think here it is easier for me to start.
I wrote myself a programm which do the calculations of the Pocket Cube. Its output is besides the count of the positions a text file where all local maxmia positions are listed with a sequence to reach it.
I picked out all 14 qtm sequences printed them out. Then i started to moved my cube to the first position. I rotated the cube to an other view, analysed the 'new' postion and marked it on the list as an equal positon.
So i could reduce the 276 antipodes to 16 positions. 14 of them can be seen as a pair. Seeing the positon in a mirror you will have an other positon. First my list. A letter to 'name' them; the sequence; in brackets the amount of positions you get when you turn the scrambled cube

A: U R U' R F' U R' U F' U F R' U2 (12)
B: R2 U R U' R F' U R' U2 R' U2 (24)
C: U' R' U' R U' F R' U R' F U F' U2 (24)
D: F2 U2 F U' F R F' R U' R' U2 (12)
E: U R' F R' U' R' U' F2 R' U R' U2 (12)
F: F2 U' R' U' R F U' F' U F R' U2 (24)
G: R' F R' U R' U F' R' F U2 R' U2 (24)
H: R' F U F' R F2 R' U R' U' R U2 (4)
I: U R' U F' R' F U' R F' R' U' R' U2 (8)
J: U F' R F' R F2 R' U R U R' U2 (8)
K: R' F' R U' R' F' R F' R U' F R' U2 (24)
L: R U R F' U F2 U' R F' U' R' U2 (4)
M: U' F R' U R' F2 R F2 U' R U2 (24)
N: R U F' U R' F R F' U' R' U R' U2 (24)
O: U R' F U' R' F R2 F' R' U R' U2 (24)
P: F U' R' F' R F2 R' U' R' U R' U2 (24)

the pairs are: B-C / D-E / G-K / H-L / I-J / M-P / N-O
H-L are the pattern "6 flags" and can be faster done with this sequence: U F2 U F2 U2 R2 U R2 U


My knowledge of math is not so good, that i know what M+ symetry means (so maybe my comment is wrong), but on the list of the 42 up there - from my view - the first, third and fourth sequence are equal:
I am using the colors of my cube - some other cubes my vary:
U: white / F: red / R: blue
B: purple / D: yellow / L: green
If you are doing the first sequence holding the cube with the colors i listed and then turn the scrambled cube, so that these colors are on the DBL position : B: yellow / D: purple / L: blue and then do the third sequence backwards, you get a solved cube. The same will happen with the fourth sequence backwards if the DBL cube is: B: green / D: red / L: white
(on my list it is positon F)

2x2x2 antipodes

You are right. The above post is in error. I revisited this question in a later post:

2x2x2 Cube

In the later post I found I could reduce the 276 antipodes to 8.