Archives

At last, I have completed my God's algorithm calculation for the 4x4x4 supercube squares group, in the single-slice half-turns only metric. It was found to have 47,968,768 antipodes, many more elements than are in the entire 3x3x3 supercube squares group. (OK, it's only 11,992,192 antipodes after reducing the group by four cube orientations.) The analysis showed that the elements in the group can always be solved using no more than 20 half-turns, only one more half-turn than the number required if the four centers for each face are considered indistinguishable. (The 4x4x4 supercube differs from the usual 4x4x4 cube in that all 24 centers are considered to be distinguishable from one another.)