# 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

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